Final

Question 1

What is the Poisson-Boltzmann model?

Answer 1

Describes mobile charges (i.e. ions in solution) around a charged object (i.e. DNA/RNA). Combine the Poisson equation
nabla^2 Phi = - rho(vec(r))/ (epsilon epsilon_0)
with a Boltzmann factor for the local concentration of mobile ions:
c(vec(r)) = c_bulk exp(-(z e Phi(vec(r)))/(k_B T))

Question 2

What is a key result of the PB model?

Answer 2

The electrostatic potential (and the field, and the ion density) fall off exponentially:
Phi(vec(r)) propto exp(-r/lambda_D)
With the Debye length as the scaling parameter

Question 3

How much is the Debye length?

Answer 3

~ 1nm in physiological salt

Question 4

What are the assumptions / simplifications in the PB model?

Answer 4

• Mean field model consider ion density, not discrete ions. Neglect ion-ion correlations.
• Only ion valency matters. E.g. all monovalent ions are the same in PB.
• Solvent is treated as simply dielectric. No explicit solvent, no polarizability.

Question 5

What is SAXS? What does it measure?

Answer 5

SAXS = small angle X-ray scattering, is a solution scattering technique. It uses X-rays from a synchrotron or in-house/lab X-ray source and looks at X-rays scattered off molecules in solutions. It gives information about the size, shape, and in some cases sub-structure of macromolecules and their complexes.

Question 6

What is the Guinier approximation in SAXS?

Answer 6

The Guinier approximation is for monodisperse samples and approximates the scattering at very low momentum transfer q (= 4 pi sin(theta) / lambda
where theta is the scattering angle and lambda is the X-ray wavelength) as
lim (q -> 0) I(q) approx I(0) exp(-q^2 R_g^2/3)
Rg is the radius of gyration and I(0) the forward scattering, which is related to the molecular mass of the scattering molecule

Question 7

How well does PB describe the effects of the real ion atmosphere around DNA?

Answer 7

For “general” properties of the ion atmosphere, e.g. its overall composition, extent around a macromolecule, ability to screen repulsion, etc. PB tens to give semi-quantitative results for monovalent ions. It does miss, however, small, but measurable differences between different monovalent ions.
For divalent ions, PB tends to give the right trends, but underestimates the ability of divalent ions to screen repulsion and compete against monovalent ions.

Question 8

What forces do single-molecule experiments work at?

Answer 8

Flow: 10^0 - 10^1 pN
Magnetic tweezers: 10^-2 - 10^1 pN
Optical tweezers: 10^0 - 10^2 pN
AFM: 10^1 - 10^3 pN

Question 9

What are the FJC and WLC models? What is the idea behind them?

Answer 9

FJC = freely jointed chain, also known as Gaussian chain or ideal chain. Perfectly rigid segments connected by perfectly flexible joints
WLC = worm-like chain. Continuous polymer with bending rigidity

Question 10

What are the parameters in the FJC and WLC models?

Answer 10

Both models have essentially two parameters:
FJC:
1) Contour length = total length = L_total = L_c = L = Nb —OR— number of segments N
2) Segment lengths = a = b = l = Kuhn length
WLC:
1) Contour length = total length = L_total = L_c = L = Nb
2) Bending persistance L_P = B = bending stiffness

Question 11

What is the Kirchhoff rod model (aka the isotropic elastic rod)?

Answer 11

Rod model with bending stiffness, twist stiffness, stretch stiffness, and twist stretch coupling, i.e. the A, B, C, D parameters.
WLC is the isotropic rod if we have free rotation (i.e. through single stranded attachment) and assume an inextensible polymer

Question 12

What techniques can be used to pull on single molecules?

Answer 12

In order of force resolution:
- Magnetic tweezers (MT) - use magnetic beads and external magnets to apply forces and torques
- Optical tweezers (OT) - use beads trapped in the focus of a laser beam
- Flow stretch - use beads acted in by a fluid flow
- AFM (= atomic force microscope) - use a small cantilever with a very sharp tip to pull on molecules

Question 13

What are the strengths and limitations of the single molecule experiments?

Answer 13

• Spatio-temporal resolution: optical tweezers and AFM that detect via photodiodes tends to sample much faster than magnetic tweezers and flow stretch, which tend to be camera based, which enhances spatio-temporal resolution.
• Magnetic tweezers can readily apply torque and twist the molecules in addition to stretching. This only possibly with special optical tweezers that have polarization control and read out and use birefringent particles
• Camera based techniques (magnetic tweezers, flow stretch) can, in general, track many molecules at the same time

Question 14

At which forces does DNA start overstretching?

Answer 14

> 50 pN

Question 15

What is the size of a cell?

Answer 15

~ 5 um

Question 16

What is the size of a protein?

Answer 16

nm scale

Question 17

What is fluorescence microscopy? How is its resolution limited?

Answer 17

Image structures labeled by fluorophores. Two main types of fluorophores: fluorescent protein (e.g. GFP = green fluorescent protein) and organic dyes (e.g. Cy3 and Cy5). Fluorophores can be excited by light and then emit light of a longer wavelength.
Resolution is limited by diffraction, Abbe’s limit:
d = lambda / (2 n sin alpha)
where d is the minimum distance resolvable between two emitters, lambda is the wavelength of light, n is the index of refraction of the immersion medium, alpha is half opening angle of the objective and n sin alpha is the numerical aperture.

Question 18

What is FRET? How does it provide a molecular ruler?

Answer 18

FRET = Förster Resonance Energy Transfer
Involves two fluorophores. One, called the donor (D), is excited, then transfer energy (non-radiatively) to the other one, called the acceptor (A), which then emits at an even longer wavelength. The transfer is very strongly dependent on the distance between the fluorophores (but also on their orientation, environment, etc).

Question 19

What are normal values for torsional stiffness for RNA and DNA?

Answer 19

~ 100 nm

Question 20

How much is 1 kBT?

Answer 20

25 meV = 4 pN nm = 0.6 kcal/mol = 2.5 kJ/mol

Question 21

How do cells store energy?

Answer 21

As chemical energy, e.g. in the form of
- ATP
- NAD+/NADH (Nicotinamide adenine dinucleotide)
- NADP+/NADPH (Nicotinamide adenine dinucleotide phosphate)
- Proton / pH gradient

Question 22

How can you think about chemical reactions in a free energy landscape? How do enzymes modify the free energy landscape of chemical reactions?

Answer 22

Free energy plot vs reaction coordinate
We start with S(ubstrate) and end with P(roduct). Both are in “wells”, with the product being in a deeper well, with a peak between them. When you add an enzyme, everything lowers (except the beginning and end which are the same) and the peak becomes less sharp. Now you start with E(nzyme)+S, go to ES for the first well, EP for the second well and E+P at the end.

Question 23

What are typical K_m and maximum rate k_cat values?

Answer 23

K_m = (k_-1 + k_2) / k_1
with S + E ->(k_1) <-(k_-1) ES ->(k_2) E + P

K_m around mM
k_cat around s^-1

Question 24

What is k_cat / K_m for diffusion limited enzymes?

Answer 24

Estimate of diffusion limited rate: k_cat / K_m = 10^9 M^-1 s^-1

Question 25

What is modeled by the Michaelis-Menten model?

Answer 25

Enzyme catalyzed reaction: Enzyme E converts substrate S to product P;
Assumptions:
- The enzyme does not get used up in the reaction ([E_0] = [E_total] = constant; [E] = [E_0] - [ES])
- Product release is fast and irreversible (no EP complex; no back reaction from E + P)

Question 26

What are the key results of the Michaelis-Menten model?

Answer 26

v_i = dP / dt = k_2 [ES] = k_2 [E_0] [S] / ([S] + K_m)
K_m = (k_-1 + k_2) / k_1
v_max = k_2 [E_0]

Same plot as for fraction bound, with V-max/2 at K_m. y reaction speed and x substrate concentration

Question 27

What are the key results of the Michaelis-Menten model?

Answer 27

v_i = dP / dt = k_2 [ES] = k_2 [E_0] [S] / ([S] + K_m)
K_m = (k_-1 + k_2) / k_1
v_max = k_2 [E_0]

Same plot as for fraction bound, with V-max/2 at K_m. y reaction speed and x substrate concentration

Question 28

How can enzymes get even faster?

Answer 28

Some enzymes break the physical “reaction speed limit”! Enzymes “steer” the substrate to the active site (e.g. electrostatically)