Biophysik

=> Dynamic viscosity describes friction in a fluid

=> friction force = force holding back the particle

- increases with increasing speed v of the particle

- friction coefficent for a neutral sphere in aqueous solution is proportional to the size of the particle (radius r) and to a material property of the solvent that is called viscosity

=> Reynold‘s number R = ratio between inertial force and frictional force

- R is small -> friction is very important, as is the case for a small molecule in aqueous solution

- R is larger -> inertia becomes more important sometimes causing turbulence in the medium. As long as no turbulence appears we have laminar movement of the fluid

=> Microorganisms swim at low Reynold‘s numbers of 10^-2 to 10^-5

-> thermal energy driving a random walk of molecules, particles (molecules collide with each other)

-> Thermal energy is determined by the Boltzmann constant kB times the temperature T —> E = kB*T

equation for the diffusion constant = Boltzmann distribution / Stokes friction coefficient

Unit: m^2/s

=> With the Stokes‐Einstein equation and the definition of particle flux (Fick‘s law) -> compute time scales for purely diffusive transport processes for various sized particles

Polymers properties:

• elasticity

• diffusion

• osmotic pressure

Hyaluronic acid: very flexible chain

Aktin, IMF: semi‐flexible filament

Collagen, mikrotubules: semi‐stiff rods

Scaling law = describes how the property changes with polymer size n

=> e.g.: scaling law for the size of single‐stranded DNA —> Scaling law: Rh ~ N^v

-> exponent v describes how much polymer segments interact with each other

-> The experiments are done with fluorescence correlation spectroscopy (FCS) in order to measure polymer size from observed diffusion processes

-> v=0.588 : 0‐solvent(ideal polymer withexcluded volume)

v>0.588 : good solven t(repulsive forces)

v<0.588 : bad solvent (attractive forces)

Flory’s characteristic ratio = alternative way of describing deviations between real polymers and the FJC model

-> describes the stiffness of polymer chains: the larger number the more stiff

= segments are assumed to be completely free – no self avoidance

-> Problem: Some features of a real polymer are not taken into account. E.g. chemical bonds typically only allow free rotation and no change of bonding angles in any direction. Furthermore, atoms cannot penetrate each other. Therefore the space occupied by one segment of the polymer can be seen as excluded volumen for other polymer segments.

• Corrections to the FJC model: Freely Rotating Chain

-> In the freely rotating chain there are fixed bond angles and variable torsional rotation angles

—> Attractive, repulsive and entropic forces can balance, such that the polymer behaves like a FJC => Cn = 1

—> All forces are influence by temperature, solvent, or other environmental conditions => A polmer is behaving ideal at the theta‐temperature or in a theta‐solvent θ

-> polymer is treated as a continuous rubber band with a certain stiffness

-> the stretched conformation (gestreckte Konformation) has the lowest energy. Any bending requires some external force (which could be due to thermal energy) —> Jede Biegung erfordert eine gewisse äußere Kraft

-> good description for semiflexible polymers where structural changes are due to competing influences from stiffness and thermal motion

• Freely Jointed Chain (FJC): n monomers of fixed length b, each having an independent orientation -> flexible polymer

• Worm‐like Chain (WLC): continuous model with persistence length, in which the orientation of the chain tangent is changing over contour lengths greater than LP -> semiflexible polymer

• Gaussian Chain: n monomers connected by harmonic springs -> very similar to FJC

single‐molecule measurements of end‐to‐end distances:

• Electronenmicroscopy

• AFM

• Force spectroscopy

-> measuring its mechanical behavior —> measure the forces needed for stretching the polymer or pulling the polymer ends apart

• Streching a polymer decreases entropie: work has to be done against Brownian motion

• The polymers response to external forces is described by molecular elasticity

= a device to manipulate dielectric particles with focused laser light

-> important in force spectroscopy

-> allow simultaneous measurement of force and extension (i.e. distance between bead and surface)

-> beads position can be visually observed in a microscope and measured at high accuracy

-> The force is determined by how much the bead is relocated from the center of the laser focus

-> Since the laser focus can be treated like a spring holding the bead in its center position, force can be determined with a good knowledge of the spring constant k (Da der Laserfokus wie eine Feder behandelt werden kann, die die Perle in ihrer Mittelposition hält, kann die Kraft mit einer guten Kenntnis der Federkonstante k bestimmt werden)

-> For a sufficently good calibration round, dielectric beads made from silicon or polystyrol are used

= spontane Emission von Licht kurz nach der Anregung eines Materials durch Licht. Dabei sind die emittierten Photonen in der Regel energieärmer als die vorher absorbierten

= property of certain substances to absorb light energy at one wavelength (usually shorter, higher energy light) and then emit light at a longer wavelength (lower energy light)

= refers to the process by which a fluorescent molecule loses its ability to emit light after being exposed to intense light, typically of a specific wavelength

1. Absorption of Light: When a fluorescent molecule absorbs light (laser in fluorescence microscopy) at its excitation wavelength, it enters an excited state

2. Emission of Light: In the excited state, the fluorescent molecule can emit light at a longer wavelength (lower energy), which is detected and used for imaging in fluorescence microscopy

3. Photobleaching: However, when a fluorescent molecule is exposed to intense light for an extended period, it can undergo irreversible chemical changes that prevent it from returning to its ground state and emitting light. As a result, the fluorescence signal from the molecule reduces over time, leading to a decrease in image quality and potentially affecting the accuracy of quantitative measurements

=> E.g. Contribution of Reactive Oxygen Species to the Photobleaching of Organic Fluorophores

=> Strategies to mitigate photobleaching: reducing the intensity and duration of illumination, using fluorescence dyes with higher photostability, and implementing techniques such as fluorescence recovery after photobleaching (FRAP) to study dynamic processes while minimizing photobleaching effects

= experimental technique to study the movement and dynamics of molecules within living cells

Principle of FRAP

1. Fluorescence Labeling: Molecules of interest within a cell or a biological sample are tagged with a fluorescent marker. This can be achieved using fluorescent proteins (like GFP) or fluorescent dyes

2. Photobleaching: A specific region of the sample is subjected to a high-intensity laser beam, which causes the fluorescent molecules in that area to lose their ability to fluoresce

3. Recovery Monitoring: After photobleaching, the sample is continuously monitored to observe the movement of non-bleached fluorescent molecules into the bleached area. The recovery of fluorescence in the bleached region is recorded over time —> Monitor the return of fluorescence in the bleached area using time-lapse microscopy

4. Data Analysis: The rate and extent of fluorescence recovery are analyzed to derive quantitative information about molecular mobility, including diffusion coefficients and binding interactions

Applications of FRAP

1. Membrane Dynamics: Studying the lateral mobility of proteins and lipids within cellular membranes.

2. Protein-Protein Interactions: Investigating the binding and dissociation rates of protein complexes.

3. Intracellular Transport: Analyzing the movement of organelles and vesicles within the cytoplasm.

4. Gene Expression Studies: Understanding the dynamics of transcription factors and other nuclear proteins.

5. Drug Discovery: Evaluating the effect of drugs on molecular mobility and interactions within cells

Advantages of FRAP

• Non-Invasive: Allows the study of live cells without disrupting their normal functions.

• Quantitative: Provides precise measurements of molecular dynamics.

• Versatile (Vielseitig): Can be applied to various biological systems and different types of molecules.

Limitations of FRAP

• Photodamage: High-intensity laser used for bleaching can cause damage to the cells.

• Complex Analysis: Data interpretation can be challenging and often requires sophisticated mathematical modeling.

• Limited to Fluorescent Molecules: Only applicable to molecules that can be fluorescently tagged.

= a class of proteins that can absorb light at specific wavelengths and then emit it at longer wavelengths

—> Direct genetic labeling of target proteins in cells

- Green Fluorescent Protein (GFP): Originally derived from the jellyfish Aequorea victoria

- Enhanced GFP (eGFP): a brighter and more photostable variant of GFP, often used in various applications

- Red Fluorescent Proteins (RFPs): Derived from various marine organisms, these proteins emit red light —> mCherry (Discosoma species) and DsRed are popular examples

Applications of Fluorescent Proteins

1. Live-Cell Imaging: FPs allow real-time visualization of cellular processes in living cells, tissues, and organisms. They can be used to tag proteins, organelles, and other cellular structures.

2. Protein Localization: FPs are fused to proteins of interest to study their localization and movement within cells. This helps in understanding protein function and interactions.

3. Gene Expression Studies: FPs can be used as reporters to monitor gene expression levels in real time. The intensity of fluorescence correlates with the activity of the promoter driving FP expression.

4. Fluorescence Resonance Energy Transfer (FRET): FRET uses pairs of FPs to study protein-protein interactions, conformational changes, and other molecular events at close proximity.

5. Fluorescence Recovery After Photobleaching (FRAP): As mentioned earlier, FPs are critical for FRAP experiments to study the dynamics of molecular diffusion and interactions.

6. Super-Resolution Microscopy: Advanced imaging techniques like STORM and PALM utilize FPs to achieve resolutions beyond the diffraction limit of light microscopy.

= advanced optical microscopy technique that allows for high-contrast imaging of events occurring at or near the cell membrane

—> By exploiting the phenomenon of total internal reflection, TIRF selectively illuminates and excites fluorophores in a thin region of the sample, typically within 100-200 nm from the glass-water interface, making it particularly useful for studying membrane dynamics, cell-substrate interactions, and molecular events at the cell surface.

Principles of TIRF Microscopy

1. Total Internal Reflection: When light traveling through a medium of higher refractive index (e.g., glass) hits an interface with a medium of lower refractive index (e.g., water or cytoplasm) at an angle greater than the critical angle, it undergoes total internal reflection. This generates an evanescent wave that penetrates a short distance into the lower refractive index medium.

2. Evanescent Wave: decays (zerfällt) exponentially with distance from the interface, typically exciting fluorophores within a few hundred nanometers of the interface. This selective excitation results in high-contrast images with minimal background fluorescence from deeper within the sample.

= powerful spectroscopic method for measuring distances in the 2-10 nm range

—> It relies on the non-radiative transfer of energy from a donor fluorophore to an acceptor fluorophore, which occurs when the two are in close proximity (2-10 nm)

—> provide valuable information about molecular interactions, conformational changes, distances within and between proteins

Principles

1. Energy Transfer: FRET occurs when the excited-state energy of a donor fluorophore is transferred to a nearby acceptor fluorophore through dipole-dipole coupling. This transfer is highly distance-dependent, making FRET a sensitive molecular ruler for nanoscale distances.

2. Spectral Overlap: The emission spectrum of the donor fluorophore must overlap with the excitation spectrum of the acceptor fluorophore for efficient energy transfer.

3. Efficiency: The efficiency of energy transfer (𝐸) is described by the Förster equation:

-> R0​ = Förster distance (the distance at which energy transfer efficiency is 50%)

-> 𝑟 = actual distance between the donor and acceptor

Example

=> Recovery after Acceptor Bleaching (FRAP) => monitoring the recovery of fluorescence in the acceptor molecule after it has been photobleached, which can provide insights into molecular interactions and dynamics

=> Avoid Synchronization of Ensembles to study conformational changes => Single-molecule FRET (smFRET)

-> offers detailed insights into the heterogeneity and dynamics of molecular processes

-> Single-Molecule Sensitivity: smFRET measures FRET efficiency at the level of single molecule pairs, providing information about individual molecular events and conformational states

Alternating Laser Excitation (ALEX) spectroscopy = used in smFRET to improve the accuracy and reliability of FRET measurements

-> By alternately exciting the donor and acceptor fluorophores, ALEX allows for the direct measurement of both donor and acceptor fluorescence intensities, as well as the identification of fluorescent molecules that contain both fluorophores

-> This approach helps to distinguish (unterscheiden) between true FRET events and other fluorescent signals, such as those from donor-only or acceptor-only species

Principles of ALEX

1. Alternating Excitation: the excitation light source alternates between two wavelengths — one that specifically excites the donor fluorophore and another that specifically excites the acceptor fluorophore. This alternation occurs rapidly, typically on the millisecond timescale

2. FRET Efficiency Measurement: By measuring the fluorescence intensities of the donor and acceptor during their respective excitation periods, ALEX allows for precise calculation of FRET efficiency (𝐸)

3. Stoichiometry Measurement: ALEX also provides information about the presence of donor-only, acceptor-only, and donor-acceptor (FRET-capable) species, allowing researchers to determine the labeling stoichiometry

Correlative EM & dSTORM —> 10 nm

dSTORM —> 100 nm

STED mocrsocopy —> 10 µm

Lattice Light-Sheet mocroscopy —> 100 µm

1. Deconvolution Microscopy

-> Recalculate the true structure

-> Knowing the PSF, deconvolution algorithms allow to compute are constructed image with improved resolution

Problems

• PSF is not known in all details

• Noise is a stochastic process

• Large computation capacity is required

2. Confocal fluorescence microscopy

• smaller pinhole -> better resolution

• but limitations in the signal-noise-ratio (SNR)

3. Two-photon microscopy

• Further decrease the noise level

4. Image scanning microscopy (Airy scan microscopy)

• improves confocal resolution by ~ 40%

• The distribution of the emitted light is imaged simultaneously for every position of the excitation focus in the sample. The image is then reconstructed by pixel re-assignment

• Resolution extension through the moiré effect —> transform the high frequency informations

• superposition of high-frequency periodic structures produce a down-modulation of the frequencies

• Relies on multiple acquisitions and computation-intensive postprocessing

• Image Nuclear Pore Complex

• Lateral resolution:~80 nm

• allows: multicolor, 3D, live cell

• requires a doughnut-shaped intensity profile —> Focal spots in the middle

• BUT: the illumination to excite fluorescence can kill cells —> If the radiation intensity is too high, it will kill the cells

Photoactivated Localization Microscopy (PALM)

-> PA-GFP (photoactivatable green fluorescent protein) can be activated by UV light from a non-fluorescentstate to a fluorescent state —-> selective for labeling of proteins & cells

-> 1. photoavctivate molecules -> 2. Image activated molecules -> 3. localize molecules -> 4. photobleach & record positions

Stochastic Optical Reconstruction Microscopy (STORM)

-> Photoswitching of organic dyes by thiols

-> On or off stage depends on oxygen levels

-> On-rate: •Oxygen concentration (250 µM) •Thermal stability

-> Off-rate: • Excitation intensity • concentration of reducing agents

Point Accumulation for Imaging in Nanoscale Topography (PAINT)

-> Able to detect more photons

-> Resolution about 7-12 nm

-> Illuminate only a small area -> fluorescently labelled probes diffuse in a solution and start to fluoresce upon binding to the object of interest

• hydrogels are used for swelling

• expand the whole sample and then labeling

• Measure the whole cell, single cell analysis -> 25-nm-resolution imaging

1. Fixation

2. Labeling: labeled biomolecules are covalently attached to a swellable polymer network

3. Gelation/digestion: sample is embedded in a dense, highly cross-linked polymer gel

4. Expansion

Fab fragment (~50 kDa)

• linkage error ~6 nm /each

• modulators of functionality

pAB/sAB (~150 kDa)

• linkage error ~15 nm /each

• modulators of functionality

Nanobodies

• commercially available

• linkage error ~4 nm

• Similar affinity

• Higher penetration

• High stability

• Easy to modify

mEOS family

• similar size as FPs (-25 kDa)

• compatible with SMLM(photoconvertible)

• linkage error ~ 5 nm

Fluorescent proteins

• easy accessible (genetic encoding)

• moderate size (-27 kDa)

• linkage error ~5 nm

• terminal labeling

• Fusion proteins

• Contain chromophore (formed by multiple aa)

• Cover broad spectral range (UV to NIR)

• Can be modulated (e.g. photoactivation or photoswitching)

• Can be used as sensors (environment,proximity, …)

SNAP/HALO/protein tags

• similar size as FPs (-25 kDa)

• compatible with org. fluorophores(photoconvertible)

• linkage error ~ 5 nm

HaloTag -> derived from the haloalkane dehalogenase enzyme DhaA from Rhodococcus rhodochrous

-> Chloroalkane reactive linker (HTL)

SNAP tag -> O6-alkylguanine-DNA-alkyltransferase (hATG)

-> O6-benzylguanine (BG)

CLIP tag -> O6-alkylguanine-DNA-alkyltransferase (hATG)

-> O2-benzylcytosine (BC)

Affimers

• based an natural proteins (e.g. Stefin A)

• Two loops form binding surface

• Variablized binding loops

• No intrinsic cysteines (disulfidbonds)

Aptamer

• single-stranded nucleic acid molecules, typically RNA or DNA

• bind to specific target molecules with high affinity and specificity

• involves conformational recognition

1. How to introduce a unique amino acid?

• Genetic Code Expansion

-> Einführung neuer, nicht-kanonischer Aminosäuren (ncAAs) in Proteine —> post-translationale Transkription

-> Ein orthogonales tRNA/Synthetase-Paar aus einer tRNA und einer Aminoacyl-tRNA-Synthetase, das spezifisch für die ncAA ist —> nicht mit den natürlichen tRNAs und Synthetasen des Wirtsorganismus interagiert

—> Diese tRNA wird von der orthogonalen Synthetase spezifisch mit der ncAA beladen

—> Stoppcodon (oft UAG = "Amber"-Codon) wird in die DNA-Sequenz des Zielproteins eingeführt, an der Stelle, wo die ncAA eingebaut werden soll -> orthogonale tRNA erkennt dieses Stoppcodon und bindet es, wodurch die ncAA ins Protein eingebaut wird

—> Zielprotein mit dem eingefügten Stoppcodon wird exprimiert und detektiert

2. How to specifically attach a fluorophore?

• Click Chemistry: Photoclick Cycloaddition, CuAAC, SPACC, SPIEDAC

-> Bioconjugation: couple 2 molecules together

—> Reactions:

• Oxime Ligation

• Staudinger Ligation

• Native Chemical Ligation

• Unnatural Motifs

• Cycloadditions: 1,3-dipolar Cycloadditions, CuAAC, SPAAC, Diels-Alder Cycloaddition, Photoinduced Tetrazole-Alkene Cycloaddition

- Time averaging analysis of spontaneous fluctuations of fluorescence signals dF

• Autocorrelation function: compares fluorescence signals ofsingle species with themselvesfor different lag times

• Crosscorrelation function: compares fluorescence signals ofdifferent species in the samemanner