PHYM008 Physical Methods in Biology & Medicine Flashcards
(191 cards)
1
Q
Define additivity in words
A
The response to the sum of 2 inputs = the sum of the response of each input mathematically.
2
Q
Define additivity mathematically
A
S(f1 + f2) = S(f1) + S(f2)
3
Q
Define homogeneity in words
A
Scaling the input by a constant factor results in the output being scaled by the same factor.
4
Q
Define homogeneity mathematically
A
S(αf) = αS(f) where α is a scalar constant
5
Q
What properties must a measurement system S satisfy to be linear
A
Additivity and homogeneity (scaling)
6
Q
Define shift/time-invariance
A
A measuring system is shift/time-invariant if a time shift in the input signal results in the same time shift in the output signal, without changing the shape of the output.
7
Q
Define shift/time-invariance mathematically
A
S(f(t-τ)) = S(f) = g(t-τ) where τ is an arbitrary time shift
8
Q
How can you test the shift-invariance in an optical imaging system?
A
- Use a known test target eg a regular grid
- Capture an image of the target at one position
- Shift the target by a known distance along the x or y axis
- Take a second image
- Compare corresponding parts of the two images: If the system is shift-invariant the images should be identical apart from the shift. Any differences (blurring, distortion) may indicate shift-variance due to lens aberrations or system misalignment.
9
Q
What can cause shift variance in an optical imaging system
A
- Optical/lens aberrations
- Vignetting (light falloff at edges of FOV)
- Lens design limitations (eg perspective distortions)
10
Q
Define convolution mathematically
A
(f * h)(t) = ∫[-∞, ∞] f(τ)h(t-τ)dτ where τ is the integration variable
11
Q
Define convolution in words
A
The integral of the product of two functions after one is reversed and shifted.
12
Q
Calculate the convolution of h(t) with itself e.g. g = h*h
A
Take the impulse response h(τ)
Horizontally flip: h(-τ)
Shift its centre to time t: h(t - τ)
You’re given h(t) = {0 t<0 1 t>0 etc
Construct same for h(τ) and h(t - τ) by replacing eg t<0 by t-τ<0
Simplify these eg t-τ<0 = τ>t
Find the inequalities where h(τ) and and h(t - τ) is non-zero (=1) for case 1 t<0 and case 2 t>= 0
If the inequalities are simultaneously possible, edit and solve the convolution integral. Therefore give g(t) = … for case 1 or 2 (eg t<0).
Combine g(t) = to give both cases ie g(t) = {… t<0 … t>=0
13
Q
Calculate the convolution of f * h at a particular time t
A
Take the impulse response h(τ)
Horizontally flip: h(-τ)
Shift its centre to time t: h(t - τ)
You’re given h(t) = {0 t<0 1 t>0 etc
Construct same for h(t - τ) by replacing eg t<0 by t-τ<0
Simplify these eg t-τ<0 = τ>t
Find the inequalities where f(τ) and h(t - τ) is non-zero (=1) for case 1 t<0 and case 2 t>= 0
If the inequalities are simultaneously possible, edit and solve the convolution integral. Therefore give g(t) = … for case 1 or 2 (eg t<0).
Combine g(t) = to give both cases ie g(t) = {… t<0 … t>=0
14
Q
Define the Fourier transform mathematically
A
f̂(v) = ℱ{f(t)} = ∫[-∞, ∞] f(t)e^(-2πitv) dt
Where f̂(v) is the Fourier transform of f(t), usually a complex-valued function of frequency ν.
15
Q
Define the Fourier transform in words
A
The Fourier transform operation ℱ transforms a function f(t) from the time domain to the frequency domain, resulting in a function f̂(v).
16
Q
Define the inverse Fourier transform in words
A
The inverse Fourier transform operation ℱ^-1 transforms a function f̂(v) from the frequency domain back to the time domain, recovering the original function f(t).
17
Q
Define the inverse Fourier transform mathematically
A
f(t) = ℱ^-1{f̂(v)} = ∫[-∞, ∞] f̂(v)e^(2πitv) dv
Where f(t) is the original function in the time domain.
18
Q
What are the difference between the normal and inverse Fourier transform mathematically
A
FT: f̂(v) = ℱ{f(t)} = ∫[-∞, ∞] f(t)e^(-2πitv) dt
IFT: f(t) = ℱ^-1{f̂(v)} = ∫[-∞, ∞] f̂(v)e^(2πitv) dv
- notation FT: f̂(v) = ℱ{f(t)} IFT: f(t) = ℱ^-1{f̂(v)}
- all t in FT replace by v in IFT
- exponential power +ve in IFT -ve in FT
- dt FT dv IFT
19
Q
What does the Fourier transform, f̂(v), represent
A
f̂(v) is complex, it represents amplitude and phase at frequency v.
20
Q
A specific signal is the shifted δ-function δ_τ(t) i.e. a δ-function with a peak at time τ. Give an expression for δ_τ(t) in terms of δ(t) and τ.
A
δ_τ(t) = δ(t - τ)
21
Q
Define the Dirac delta function mathematically
A
δ(t - τ)
22
Q
Define the Dirac delta function in words
A
An idealised impulse that is infinitely tall and narrow representing an instantaneous event (eg a perfect spike at time t = τ) but its area is normalised to 1.
23
Q
Give the 2 key properties of the Dirac delta function δ(t - τ)
A
- Zero everywhere except t = τ
- Integration normalised to 1
∫[-∞, ∞] δ(t - τ) dt = 1
24
Q
Give 2 key applications of the Dirac delta function δ(t - τ)
A
- Sampling/sifting property: extracts the value of f(t) at t=τ
- Impulse response in systems theory: used to model instantaneous perturbations (eg hammer strike in mechanics).
25
Explain the sampling/sifting property of the Dirac delta function, giving the equation
∫[-∞, ∞] f(t)δ(t - τ)dt = f(τ)
As δ(t - τ) is zero everywhere except t=τ, the product f(t)δ(t - τ) is also zero everywhere except t=τ. As the integral of δ(t - τ) is 1, the only contribution to this integral comes from f(t) evaluated at t=τ.
26
What is the magnitude of any complex exponential of the form e^ix
1
Eg | e^-2πiτv | = 1
27
What is the phase of any complex exponential of the form e^ix
The exponent of the imaginary exponential ie e^ix phase is x
Eg phase of e^-2πiτν = -2πτν
28
Explain the teleport property of the delta function in convolution
Any function convolved with δ(t-τ) teleports the function to its position on the t axis, replacing the t variable in the original function with its t-τ
For example:
g(t) = f(t/T) * δ(t-(nT)/2)
g(t) = f((t-(nT)/2)/T);
29
∫e^2x =
(e^2x)/2 + c
30
Define Euler's formula mathematically
e^iφ = cos φ + i sin φ
31
e^iφ =
cos φ + i sin φ (Euler's formula)
32
sinc(v) =
sin(v)/v OR sin(πν)/πν
33
What's the Fourier transform pair rule
f(t) ⇔ f̂(v), then f̂(t) ⇔ f(-v)
34
Define a function being even
The function is symmetrical across the y axis i.e. f(x) = f(-x).
35
Define a function being odd
The function has rotation symmetry around the origin (looks the same if you rotate it 180° about the origin) i.e. f(-x) = -f(x).
36
Define bandwidth
The range of frequencies over which a system operates or a signal contains significant energy.
37
Define Förster Resonance Energy Transfer (FRET) efficiency mathematically
E = (R_0^6)/(R_0^6 + r_DA^6)
where E: FRET efficiency (dimensionless, %)
R_0: Förster radius (distance at which E = 50%)
r_DA: Distance between donor and acceptor molecules.
38
What's R_0
Förster radius: distance at which FRET efficiency E = 50%.
39
Define bandwidth of a signal
The difference between the highest and lowest frequencies where the signal's Fourier transform is non-negligible.
40
Define spatial bandwidth
The range of spatial frequencies a signal (eg an image) contains.
41
How do spatial bandwidth limits arise in an imaging system
They primarily arise from:
1. Diffraction: wave nature of light restricts the finest resolvable detail
2. Point spread function (PSF): the microscope's point spread function (PSF) acts as a Fourier filter, attenuating high spatial frequencies (fine details)
3. Detector sampling: pixel size must satisfy Nyquist criterion otherwise aliasing further reduces effective bandwidth
4. Noise and signal to noise ratio: high frequency signals (fine details) may be lost if they fall below noise levels.
42
Define point spread function (PSF)
The image of a single point source, describing how an optical system blurs/distorts a signal/light (due to diffraction and aberrations).
43
Define optical transfer function (OTF)
The Fourier transform of the PSF, quantifying how the system attenuates different spatial frequencies.
44
Sketch the dependence of FRET efficiency E (%) on distance between donor and accept molecules r_DA (nm)
E (%) against r_DA (0-10 nm)
——
-
-
- R0 (50%)
-
————
45
Define crosstalk
Unwanted transfer of signals or information from one communication channel to another.
46
Describe 2 different ways in which FRET efficiency can be measured
1. Fluorescence Lifetime-based measurement
FRET reduces the donor's fluorescence lifetime (τ_D) because energy transfer provides an additional decay pathway.
Advantage: insensitive to concentration and excitation intensity.
2. Spectral Intensity Measurements (Donor/Acceptor Emission)
Measure changes in donor quenching (decrease in donor fluorescence intensity) or acceptor sensitisation (increase in acceptor fluorescence).
Challenge: requires correction for crosstalk (donor signal in acceptor channel) and bleed-through (visa verca).
47
Give 2 examples of applications of FRET microscopy.
1. Measuring conformational changes in proteins
Label 2 domain of a protein with donor and acceptor. FRET efficiency changes as protein shifts between open/closed states (eg Ca2+ binding). E.g. monitoring GPCR activation by measuring distance changes between transmembrane helices.
2. Detecting protein-protein interactions (eg mitochondrial proteins)
Tag 2 potentially interacting proteins with donor/acceptor. FRET occurs only if proteins are within ~1-10 nm, confirming association. High FRET efficiency = close proximity low FRET efficiency = no interaction.
48
Describe the principles of Fluorescence Recovery after Photobleaching (FRAP) microscopy
1. Photobleaching: A high-intensity laser beam is used to irreversibly bleach (destroy) fluorescent molecules in a defined region of the sample.
2. Recovery monitoring: Sample then imaged with low-intensity illumination to track return of fluorescence into bleached area due to: diffusion of unbleached molecules and binding/unbinding dynamics.
3. Quantitative analysis: recovery curve is fitted to extract: mobile fraction (% of molecules that can diffuse into bleached zone) & diffusion coefficient (how fast molecules move).
49
Explain what properties of a biophysical system Fluorescence Recovery after Photobleaching (FRAP) microscopy can probe
1. Mobility of molecules (eg lipids, proteins, RNA)
2. Binding kinetics (eg protein-DNA interactions)
3. Membrane fluidity (eg lipid bilayer dynamics).
50
Give an example application of Fluorescence Recovery after Photobleaching (FRAP) microscopy
Lipid mobility in membranes
Label membrane lipids with fluorescent dye (eg Dil), bleach small spot on membrane and monitor fluorescence recovery.
Fast recovery = high fluidity
Slow/no recovery = restricted mobility.
51
Define Rayleigh criterion mathematically
d = 0.61λ/NA
Where d: Rayleigh criterion: smallest resolvable distance between 2 point sources.
52
Define Rayleigh criterion in words
Smallest resolvable distance d between two point sources.
53
What does an objective lens labeled with this mean: Plan Apo 100/1.25 Oil 160/0.17 WD 0.21
Plan: flat-field correction
Apo: aberration correction
100: 100x magnification
1.25: numerical aperture
Oil: immersion medium
160/0.17: tube length nm/coverslip thickness mm
WD 0.21: working distance mm.
54
What does an objective lens labeled with this mean: Plan Fluor 60/0.85W ∞/0-0.17/FN26.5 WD 0.21
Plan Fluor: flat field / aberration correction
60/0.85W: Magnification / numerical aperture / water dipping or immersion objective
∞/0-0.17/FN26.5: infinity correction/coverslip thickness mm/field number
WD 0.21: working distance mm
Adjustable ring: correction ring.
55
Give the general equation for lateral resolution and then the specific examples
(Full width at half maximum) FWHMxy = Cλ/NA
Fluorescence microscopy: either r0 = 0.61λ/NA (Rayleigh criterion) or C = 0.51 (FWMH)
Confocal microscopy: C = 0.37.
56
Define Nyquist Criterion
The Nyquist-Shannon sampling theorem states that to accurately reconstruct a signal, the sampling rate must be at least twice the highest spatial frequency present.
57
Why is high NA objective often desirable
Increase resolution (FWMHxy = Cλ/NA): finer details can be resolved
Better signal to noise ratio: enabling detection of faint structures like small vesicles.
58
Why does TIRF microscopy require a high NA objective
A high NA is required to achieve the steep angles needed for TIR to produce the evanescent wave required in TIRF.
59
What does the Nyquist-Shannon sampling theorem state?
To accurately reconstruct a signal, the sampling rate must be at least twice the highest spatial frequency present.
60
Why is a high NA objective often desirable?
It increases resolution (FWMHxy = Cλ/NA) and provides a better signal to noise ratio, enabling detection of faint structures like small vesicles.
61
Why does TIRF microscopy require a high NA objective?
A high NA is required to achieve the steep angles needed for total internal reflection to produce the evanescent wave required in TIRF.
62
What are the trade-offs to using a high NA?
Shorter working distance (may limit imaging depth in thick samples) and higher cost and complexity.
63
What is a high but achievable numerical aperture (NA)?
1.4 (oil immersion objective), 1.3 (water), 1.0 (dry/air).
64
What is the general equation for axial resolution?
(Full width at half maximum) FWHMz = Cnλ/(NA^2)
## Footnote
Fluorescence microscopy: C = 1.77; Confocal microscopy: C = 1.28.
65
How do you calculate pixel size for adequate spatial sampling?
According to the Nyquist criterion, the effective pixel size of the detector should be at most half the smallest resolvable feature size (calculated via Rayleigh criterion).
66
Define Nyquist criterion mathematically.
Pixel size <= resolution/2.
67
Given average photoelectron number, how do you estimate standard deviation of counts due to photon shot noise?
Standard deviation, σ = sqrt(μ) = sqrt(mean photoelectrons per pixel).
68
What statistical distribution describes photon shot noise distribution?
Poisson distribution.
69
Provide the formula for the probability of recording n photons when the average photon count is N.
P(n) = (N^n)(e^-N)/n!
## Footnote
Where N: mean number of photons detected, n: actual number of photons recorded, e: Euler's number.
70
What noise sources typically contribute to noise in camera recordings?
1. Photon shot noise: Caused by unavoidable random process of the arrival of photons at the camera sensor.
2. Read(out) noise: Noise introduced by the electronics during signal measurement.
3. Dark noise: Caused by thermal excitation of electrons in sensor.
4. Fixed pattern noise (FPN): Caused by non-uniform pixel sensitivity.
5. Gain multiplication noise: Caused by stochastic nature of electron multiplication.
71
What's photon shot noise?
Caused by unavoidable random process of the arrival of photons at the camera sensor.
72
What's read noise?
Caused during conversion of electrons to a digital signal.
73
What's dark noise?
Caused by thermal excitation of electrons in sensor, generating false signals even in darkness.
74
What's fixed-pattern noise (FPN)?
Caused by non-uniform pixel sensitivity or slight manufacturing variations.
75
What's gain multiplication noise?
Caused by stochastic nature of electron multiplication, adding extra variance beyond poisonous stats.
76
What's the optical principle of total internal reflection fluorescence (TIRF) microscopy?
Uses total internal reflection (TIR) at the coverslip-sample interface to generate an evanescent wave which penetrates ~100nm from coverslip.
77
How far does the evanescent wave penetrate in TIRF microscopy?
~100nm from coverslip.
78
What's the optical principle of confocal microscopy?
Uses a pinhole in front of the detector to reject out of focus/scattered light, improving contrast and resolution.
79
What is the primary use case for TIRF?
Membrane dynamics and single-molecule imaging.
80
What is the primary use case for confocal microscopy?
3D cellular imaging and thick samples.
81
What are the stages of single particle cryogenic electron microscopy (cryo-EM)?
1. Sample prep (cryogenic preservation) 2. TEM imaging 3. Computational 2D alignment and averaging 4. Reconstruct 3D density map 5. Atomic model fitting.
82
Describe stage 1 of cryo-EM.
Sample prep (cryogenic preservation) involves rapid vitrification of the protein sample in liquid ethane (~-180°C).
83
Describe stage 2 of cryo-EM.
TEM imaging involves inserting the frozen sample into a TEM under cryogenic conditions.
84
Describe stage 3 of cryo-EM.
Computational 2D alignment and averaging involves particle picking and grouping similar particle views.
85
Describe stage 4 of cryo-EM.
Reconstruct 3D density map using tomography algorithms.
86
Describe stage 5 of cryo-EM.
Atomic model fitting can be done if resolution is high enough (better than ~3-4Å).
87
How large are typical biomolecules and biomolecular structures?
~1nm (small proteins) to several 100nm (viruses).
88
What resolution is needed to obtain atomic resolution structures of biomolecules?
~1Å (0.1nm) is required.
89
State typical value for physical dimensions of proteins.
~1-10nm diameter, depending on folding and domain structure.
90
State typical value for mass of proteins.
~10-100 kDa, as one amino acid is ~110 Da.
91
Describe what is meant by primary protein structure.
The linear sequence of amino acids in a polypeptide chain, linked by peptide bonds.
92
Describe what is meant by secondary protein structure.
Local folding of polypeptide chain into repeating patterns, stabilized by hydrogen bonds.
93
Describe what is meant by tertiary protein structure.
3D conformation of a single polypeptide chain formed by interactions between side chains.
94
Describe what is meant by quaternary protein structure.
The assembly of multiple polypeptide chains into a functional protein complex.
95
What resolution is currently achievable?
Techniques like X-ray crystallography and cryo-EM now routinely achieve <3Å.
96
How much is 1 Angstrom Å in m and nm?
1 x 10^-10 m and so 1Å = 0.1nm.
97
What's the phase problem?
The phase problem arises because we can only measure the intensities of scattered waves, losing crucial phase information.
98
What are the advantages of Cryo-EM over (X-ray) crystallography?
1. No crystallisation required. 2. No phase problem. 3. Tolerates heterogeneity & multiple conformations. 4. Near-native conditions.
99
What was the key trade-off in using cryo-EM over crystallography in the past?
Lower resolution.
100
What technical innovations in cryo-EM were critical to improving resolution?
1. Direct electron detectors (DEDs). 2. Improved beam stability. 3. Improved sample prep. 4. Computational advances. 5. Automated data collection.
101
How did direct electron detectors improve cryo-EM?
Higher sensitivity and faster readout, reducing noise and enabling single-electron detection.
102
How did beam-induced motion correction improve cryo-EM?
Algorithmic advances align frames to correct beam-induced movement.
103
How did improved sample prep improve cryo-EM?
Vitrification optimisations reduce damage/deformation and low dose imaging minimises radiation damage.
104
How did computational advances improve cryo-EM?
Better particle picking and 2D/3D classification.
105
Define volume of a cylinder mathematically.
V = πhr^2 or 0.25πhd^2.
106
Define lateral surface area of a cylinder mathematically.
A = πdh or 2πrh.
107
How would you calculate volume & surface area of mitochondria based on confocal microscopy image?
Image processing, segmentation, and V & SA calculation typically with software.
108
Why was random diffusion previously thought to set the upper limit of cell size?
Cells rely on diffusion for nutrient transport, which is slow across longer distances.
109
Why did the discovery of tightly packed substrates that hinder random diffusion alter the simple diffusion theory?
It reduced effective diffusion coefficient D, leading to stricter size limits.
110
How can cells overcome limitations of diffusion to achieve larger sizes?
Directed transport, asymmetric size, and circulation systems.
111
What is the function of the excitation filter in fluorescence microscopy?
Blocks all light except excitation bands.
112
Describe the appearance of an excitation filter transmission spectrum in fluorescence microscopy.
Mirrors excitation peaks of fluorophores but avoids overlap.
113
What is the function of the dichroic filter in fluorescence microscopy?
Wavelength selective mirror that reflects desired excitation light towards the sample.
114
Describe the appearance of a dichroic filter transmission spectrum in fluorescence microscopy.
Mirrors emission peaks and 0% transmission at excitation peaks.
115
What is the function of the emission filter in fluorescence microscopy?
Allows only the fluorescent emission wavelengths to pass through to the detector.
116
Describe the appearance of an emission filter transmission spectrum in fluorescence microscopy.
Mirrors emission peaks while blocking crosstalk.
117
What angle is the dichroic filter placed to the light path in fluorescence microscopy?
45°.
118
Rank the typical optical density (OD) required for the 3 fluorescence microscopy filters (high to low).
1. Emission filter (6-7+). 2. Excitation filter (~6). 3. Dichroic filter (~3-4).
119
Describe the physics of optical filters.
Relies on thin-film interference: light waves reflect off multiple layers of materials.
120
How are optical filters made?
Typically made by stacking 10-500+ ultra thin layers of materials.
121
What manufacturing techniques are used in optical filter production?
Physical vapour deposition (PVD), ion-assisted deposition (IAD), and sputtering.
122
Define aliasing.
A phenomenon that occurs when a continuous signal is sampled at an insufficient rate.
123
Give the equation that can be used to calculate the aliased frequency.
v_alias = |nv_s - v_1|
## Footnote
Where v_alias is the aliased frequency, v_s is the sampling frequency, V_1 is the original frequency.
124
A signal is sampled with a frequency of 2v_0. At what frequency will the original frequency content at frequency v_1 appear in the reconstructed signal?
v_alias = |2v_0 - v_1|.
125
To avoid unwanted signal artefacts/aliasing, at what frequency should the signal be sampled?
At least twice the highest frequency component of the signal.
126
If the highest sampling frequency available is not high enough, what should you do to the signal before it is sampled?
Pre-process the signal to prevent aliasing by applying a low-pass filter.
127
What's the typical size of a cell nucleus?
~5 μm diameter.
128
At what frequency should the signal be sampled?
At least twice the highest frequency component of the signal. This ensures the Nyquist criterion is satisfied.
129
What should you do to the signal before it is sampled if the highest sampling frequency available is not high enough?
Pre-process the signal to prevent aliasing: apply a low-pass filter in the analogue domain before sampling to remove frequency components above half the sampling frequency.
130
What's the typical size of a cell nucleus?
~5 μm diameter
131
What's the typical size of a mitochondrion?
0.5-1 μm diameter, 4-10 μm length
132
What's the typical size of the endoplasmic reticulum?
Tubules: 30-100 nm diameter; Sheets: 30-50 nm lumenal thickness
133
What's the typical thickness of the lipid bilayer?
5-10 nm
134
What's the typical size of a virus?
>1 μm - 30 μm
135
What's the typical size of a membrane protein?
5-10 nm
136
List microscope imaging techniques that can resolve spatial detail within mitochondria.
EM such as TEM, SEM or Cryo-EM; Super-resolution light microscopy such as stimulated emission depletion (STED) microscopy.
137
Name a type of super-resolution light microscopy.
Stimulated emission depletion (STED) microscopy.
138
State the resolution of TEM.
~0.1-0.2 nm
139
State the resolution of SEM.
~1-20 nm
140
State the resolution of cryo-EM.
Varies but can reach near-atomic resolution.
141
State the resolution of stimulated emission depletion (STED) microscopy.
~50 nm depending on depletion beam intensity.
142
State the resolution for structured illumination microscopy (SIM).
~100 nm
143
State the resolution of single-molecule localisation microscopy (SMLM).
~20 nm
144
State the resolution of widefield fluorescence microscopy.
~200-250 nm
145
State the resolution of confocal laser scanning microscopy (CLSM).
~200 nm
146
What's the principle of (linear) structured illumination microscopy (SIM)?
Linear SIM illuminates the sample with patterned light (e.g., stripes). The light interacts with fine sample structures, creating Moiré fringes that encode high-resolution information normally lost due to diffraction.
147
How is SIM able to increase resolution compared to traditional diffraction limited microscopy?
Patterned illumination shifts high spatial frequencies into the detectable range of the microscope, allowing reconstruction of a complete image with double the resolution of conventional diffraction-limited microscopy.
148
How much greater resolution are SIM images compared to light microscopy images?
Linear SIM: 2x the resolution; Nonlinear SIM: unlimited in principle (but practically limited by signal to noise).
149
What does SIM stand for?
Structured Illumination Microscopy.
150
Rank the resolutions of EM techniques (high to low).
1. TEM (0.1-0.2 nm); 2. Cryo-EM (0.1-10 nm); 3. SEM (1-20 nm).
151
Rank the resolutions of conventional optical microscopy (high to low).
1. Total internal reflection fluorescence TIRF (150 nm); 2. Confocal laser scanning (200 nm); 3. Widefield fluorescence (200-250 nm); 4. Raman microscopy (400 nm).
152
Rank the resolutions of super-resolution light microscopy (high to low).
1. Single molecule localisation microscopy SMLM (20 nm); 2. Stimulated emission depletion STED microscopy (50 nm); 3. Structured illumination microscopy SIM (100 nm).
153
What's the resolution of total internal reflection fluorescence (TIRF) microscopy?
~150 nm
154
What's the principle of Raman microscopy?
Combines optical microscopy with Raman spectroscopy: Monochromatic laser focused on sample; Small portion of incident light is scattered at a different energy due to interaction with molecular vibrations, giving rise to Raman shift.
155
Define Raman shift.
Difference in energy between incident and scattered photons/light, typically in cm^-1.
156
What does Raman shift look like on an energy level diagram?
Arrow up from ground state to virtual energy state (one stage below excited state) then smaller arrow down to vibration energy state just above ground state.
157
Which type of scattering geometry is used in Raman microscopy?
180° backscattering geometry - same objective is used to focus excitation light and collect scattered light.
158
What does SMLM stand for?
Single-molecule localisation microscopy.
159
Define Stokes shift in words.
The difference in energy (or wavelength) between the light a substance absorbs and the light it subsequently emits.
160
How do you estimate the Stokes shift of dyes given their excitation and emission spectra?
Distance between excitation and emission peaks.
161
Give 2 problems that can arise when attempting to image and localise signals from two dyes with fairly close emission spectra.
1. Overlap of emission spectra makes it hard to distinguish their fluorescent signals using standard filter sets. 2. Potential for FRET (Förster Resonance Energy Transfer) from donor to acceptor dyes if these 2 dyes are within a few nm of each other.
162
Suggest 3 approaches to distinguish the signals from 2 dyes with close emission spectra.
1. Use excitation at a compromise wavelength to partially excite both dyes. 2. Apply computational spectral unmixing techniques. 3. Measure in several emission windows to attempt to separate the 2 spectra.
163
What measurements can be performed to test how well an approach has distinguished the signals from 2 dyes with close emission spectra?
1. Use control samples stained with only 1 of the 2 dyes. 2. Use a sample where 2 spatially distinct structures are labelled. 3. Quantitatively compare the signal intensities and ratios in mixed and single labelled samples.
164
State 3 types of camera noise properties.
Read noise; Dark (current) noise; Fixed pattern noise (FPN).
165
How does read noise affect images?
Increases variance in pixel values especially under low light conditions, obscuring weak signals.
166
How does dark (current) noise affect images?
Introduces a false signal even when no photons hit detector, reducing image contrast and signal accuracy.
167
How does fixed pattern noise affect images?
Pixel to pixel variation in sensitivity that appears as a static, repeating 'grid' artefact.
168
How can read noise be reduced?
Improved amplifier and electronics design and slower readout speeds.
169
How can dark (current) noise be reduced?
Cooling camera sensor often using thermoelectric coolers.
170
How can fixed pattern noise be reduced?
Correlated double sampling (CDS): measure each pixel signal twice and subtract to cancel offset variations.
171
What's correlated double sampling (CDS)?
Method to reduce fixed pattern noise: Measure each pixel signal twice and subtract to cancel offset variations.
172
What is the name of the uncertainty associated with photon detection itself?
Photon noise (aka shot noise).
173
Define photon (/shot) noise in words and mathematically.
The fundamental randomness of photon arrival times due to quantum nature of light. It follows Poisson statistics: noise (σ) = sqrt(N) where N is (mean) number of detected photons.
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What's the standard deviation (noise) of Poisson distribution?
σ = sqrt(N)
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Derive an expression for signal to noise ratio of photon detection in terms of mean number of photons.
Signal/Noise = sqrt(N)
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Explain why noise associated with photon detection is most problematic when imaging low light level scenes.
At low N both the signal and noise are small but the relative noise is high, making image features hard to distinguish from noise.
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Give the formula for a complex number in exponential polar form.
z = re^iθ
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Give the formula for a complex number in Cartesian rectangular form.
z = x + iy
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Give the formula for a complex number in trigonometric polar form.
z = r(cosθ + i sinθ)
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What 3 forms can a complex number be written in?
Rectangular; Trigonometric polar; Exponential polar.
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What are the conversion formulas to convert a complex number from Cartesian rectangular to trigonometric polar form?
x = r cosθ; y = r sinθ.
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How can you convert a complex number in trigonometric polar form to exponential polar form?
Use Euler's formula: e^iθ = cosθ + i sinθ.
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Mathematically define the magnitude of a complex number.
r = |z| = sqrt(a^2 + b^2)
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Mathematically define the phase angle / argument of a complex number.
φ = arg(z) = arctan(b/a)
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What does magnitude mean in terms of a frequency system?
How much the system amplifies that frequency.
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What does phase angle / argument mean in terms of a frequency system?
How much delay/advance is given to that frequency.
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What issues may arise when sampling a system with no bandwidth limit?
The Nyquist-Shannon sampling theorem says you must sample at twice the highest frequency in the signal - but if there's infinite signal frequency there's no safe rate, likely leading to aliasing.
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What precautions should be taken to enable high quality sampling of a system that is not bandwidth limited?
1. Apply an analogue low-pass filter to remove frequency components above half the sampling rate. 2. Use a sufficiently high sampling rate to capture all relevant signal features.
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What areas of measurement is the Fourier Transform important?
1. Structural biology: X-ray crystallography, Cryo-EM, Structured illumination microscopy SIM; 2. Medical imaging: MRI, CT; 3. Engineering: Satellite imaging, Resonant frequencies in structures.
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Describe the relevance and use of the Fourier Transform methods in the determination of 3D protein structure.
X-ray crystallography: the diffraction pattern produced by X-rays interacting with a protein crystal is the Fourier transform of the electron density of the molecule.
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