2. Bio-energetics and molecular machines Flashcards
Free energy is…
G = U -TS
Probability of being in a state with free energy G is proportional to..
number of microstates * exp(-G/kT)
For a spontatneous process, the change in free energy is…
positive
Derive the diffusion equation
Derive Einstein’s relation by considering a random walk under a force F
Derive Einstein’s relation by considering drift velocity at low Re
Law of mass action =
the number of particles that transition between two states is propotional to teh number of available particles
J_12 = k_12 [A_1]
Principle of detailed balance =
If a system is in equilibrium then each of its degress of freedom is also in equilibrium
Dissociation constant at equilibrium is
[A][B]/[AB] = k_off/k_on = K_D
What are biological membranes made of?
Phospholipid bilayers
Describe the structure of an amphiphile
Contains a head (hydrophilic) and hydrocarbon tails (hydrophobic).
The head is either neutral or negative.
The size of the head determines how the amphiphiles self organise.
A negative head has a larger effective size.
Name the three common amphiphile phases in water and state when they are likley to form
Derive the conditions for formation of a sphere, cylinder and bilaryer
Derive the energy of a bilayer sphere
Energy to move an ion from water to hydrocarbon
e^2/(8πE_0 R) (1/E_membrane - 1/E_water
where E is epsilon
Capicitance is given by
A E_0 E_r / t
Nernst equation
C2/C1 = k12/k21 = exp(-q(V2-V1)/kT)
Derive the Poisson-Boltzmann equation
PMF is driven by
electrical potenital plus a concentraion gradient
How is pmf generated?
active transport of proteins across a membrane
What is required for the pmf to do significant work and why?
A pH gradient chemical potential because this means protons are driven by voltage and diffusion.
What is pmf usually used for?
Generating ATP
How much energy does ATP hydrolysis generate?
20-30 kT
Why do ATP bonds have high energy (3)?
- The products have a high hydration energy due to entropy, hydrogen bonding and charge shielding.
- The phosphate groups repel each other.
- Resonance - electrons can move between oxygens. In ATP the oxygen is shared so there are fewer possible arrangements -> entropy is lower than in products.
3 steps to produces ATP from glucose
- glycosis - ie oxidation of glucose
- proton pumping
- ATP synthesis - using atp synthase
2 steps of photosynthesis
- light harvesting - light is absorbed and used to make a pmf and thus ATP and NADPH
- glucose fixation - ATP and NADPH are used to make glucose. This follows Calvin cycle - roughly the reverse of the citric acid cycle
Structure of muscle tissue
Formed of repeating units called sarcomeres.
Each sarcomere contains actin filamens which slide past myosin filamens. This makes the muscle contract.
How to study actin-myosin using optical tweezers
String actin between two beads held in optical traps.
Bring myosin into contact with actin in presence of ATP.
Actin is then pulled by myosin but not continuously.
Either - keep bead still and measure force or keep force constant and measure position.
Peak force exerted by myosin
about 6pN
processive motors =
take multiple steps without detaching
How is myosin V imaged?
using electron microscopy
What are the 6 steps in the crossbridge cycle?
- ATP binds to actin which makes the mysosin release the actin. This causes the muscle to relax.
- ATP is converted to ADP and one phosphate through hydrolysis.
- The enrgy released allows the myosin to bind to the actin.
- The mysosin releases the phosphate group causing its head to relax, pulling on the actin. This retracts the muscle.
- ADP is released.
- ATP binds…
What are the two differences between chemical and mechanical transitions and therefore how can we model the crossbridge cycle?
Chemical transitions are local and fast, mecahnical are gobal and slow.
We can thus treat chemical changes as instantaneous jumps between discrete states and mechanical changes as continuous variables.
Sketch the minimal model
Derive the average force in the crossbridge model
Why does mean force reduce with speed in the crossbridge model (2)?
- Moving faster reduces binding probability
- The drag stroke is longer (where mysoin remains attached after passing energy minimum.
How is ATP symthase imaged and why is it hard?
Cryo electron microsopy using direct electron detectors. Hard because it is partly a membrane structure
Describe the F0 rotor
Consists of 7-18 subunits arranged cylindrally.
These subunits act as a turnstyle - H+ ions bind to the rotor, causing it to spin.
The subunits consist of half channels - the protons cannot pass right thorugh.
The only way for ions to cross the membrane is through being carried the whole way around the turnstile.
Describe the F1 rotor
Beta subunits are where ADP/ATP bind
Gamma subunit rotaes causing conformational change
How can the F1 rotor be studied?
Attach a visible handle
Take many images and average - several discrete states are seen.
Can change the length of the handle to see the effect of an opposing torque
Derive rate of irreversible two step process
Draw diagram of ATP synthase hydrolysis process
Why is stirring an inefficient way for bacteria to feed?
Time for transport by stirring t_stir ~ l/v
Time for transport by diffusion t_diff ~l^2/D
So for t_stir < t_diff we require
v>D/l
which is very very fast
Why is swimming better than diffusion?
For diffusion d~sqrt(t)
For swimming d~t
To outrun diffusion how far must you move in each burst?
d > D/v
How do bacteria move?
Move along concentration gradients. Bursts are longer if the gradient are steeper. Not reduced if gradient is negative.
Why do bacteria use bursts of movement?
Brownian motion regulalrly knocks them off their path.
Name and describe the two parts of bacteria motion
runs and tumbles
runs = when the bacteria moves in a single direction. most flagellar move the same way
tumbles - when the bacteria turns. Here about half of the flagellar move in each direction
Derive the equilibrium state and probabilty of being in state B for a two state reversible reaction (for second part let A_0=1, B_0=0)
Derive the probability of two sequential irreversible steps happening in time dt (where k_1 =! k_2)
