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PHYS5530M Physics of Biological Systems > Single Molecule Dynamics & Crossing Membranes > Flashcards

Single Molecule Dynamics & Crossing Membranes Flashcards

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1
Q

Single Molecule Dynamics

Overview

A
  • diffusion of single molecules is a key process in biological materials
  • thermal energy, kb*T, is effective at keeping the objects in motion and in randomising their direction
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2
Q

How can there be well-ordered structures and controlled processes in this random environment?

A
  • strong interactions, interactions&raquo_space; kb*T, but this would then require a mechanism to break the strong bonds in order for rearrangment to occur
  • non-equilibrium processes, system is maintained out of equilibrium via external fields or chemical energy (ATP) which allows them to avoid reaching thermal equilibrium
  • statistical physics, each particle moves randomly and is subject to unpredictable randomisation by kb*T, BUT the collective statistical behaviour is entirely predictable
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3
Q

Why is diffusion important in cells?

A
  • diffusion allows molecules to move without doing work
  • it allows molecules to find each other e.g. enzymes-substrates, proteins-proteins, communication through ions/signalling molecules/proteins, drug-target sites
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4
Q

Single Molecule Diffusion

A
  • molecules move because other molecules keep bumping into them
  • individual molecules follow a random walk due to these collisions
  • Brownian motion
  • diffusion is the collective motion of many molecules, many random walks by many molecules
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5
Q

Random Walks

Definition

A

-at each time step, randomly pick a direction and move one unit in that direction

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6
Q

Random Walks

Mean Displacement

A

E[x(N)] = 0

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7
Q

Random Walks

Mean Square Displacement

A

E[x(N)²] = NL²

  • where L is the step distance
  • as becomes large, the distribution approaches Gaussian with mean 0 and variance NL²
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8
Q

Diffusion as a Function of Time

A

N = t/Δt
-where N is the number of steps, t is the total time and Δt is the time step
=>
E[x(N)²] = NL² = t/Δt * L²

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9
Q

Diffusion in Cells

A 
-extend random walk to 2D and 3D
 = 2mDt
-where  is the mean square displacement
-and D is the diffusion constant 
-and m is the spatial dimension (1D,2D,3D)
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10
Q

Diffusion Examples for Different Dimensions

A

1D - proteins along DNA
2D - lipids / proteins in membranes
3D - ions / proteins within and outside cells

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11
Q

Stokes-Einstein Equation

A

D = kb*T / [6π η(T) rH]

  • where η(T) is the viscosity
  • and rH is the hydrodynamic radius of the molecule
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12
Q

Diffusion Inside Cells vs in Water

A
  • diffusion is slower inside cells
  • the viscosity of the cytoplasm is non-uniform
  • cells are highly crowded meaning there is a large excluded volume
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13
Q

Composition of Cells

A 
-in weight:
70% water
15% proteins
6% RNA
4% small molecules
2% phospholipids
2% polysaccarides
1% DNA
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14
Q

Mean Separation Between Proteins in a Crowded Environment

A

= [N/V]^(-1/3)

  • N is the number of molecules
  • V is the total cell volume
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15
Q

Typical Protein Size

A

3nm-20nm

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16
Q

Factors Affecting Protein Diffusion

A
  • collisions with crowders
  • hydrodynamic interactions
  • attractive interactions
  • immobile barriers (membranes)
  • sieving effects
  • spatial heterogeneity (different areas of the cell with differnet densities of different proteins)
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17
Q

Molecular Crowding - Excluded Volume

A
  • excluded volume is the space that the centre of the probe molecule can’t reach
  • this depends on the radius of the probe molecule, Rp, and the radius of background molecules, Rb
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18
Q

How do we measure the diffusion constant?

A
  • track proteins tagged with fluorescent molecules or track fluorescent molecules directly
  • three main techniques:
  • -fluorescence correlation spectroscopy (FCS)
  • -fluorescence recovery after photobleaching (FRAP)
  • -single particle tracking
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19
Q

Fluorescence Correlation Spectroscopy (FCS)

A
  • excites volume of space with laser
  • as molecule enters this region it is excited and fluoresces
  • molecules move in and out of the region by diffusion, this can be measured by measuring the intensity of the fluorescing molecules
  • apply autocorreltation
  • use τD = r²/4D to find D
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20
Q

Fluorescence Recovery After Photobleaching (FRAP)

A
  • quickly bleach the fluorecent dyes in a given area by shining high intensity light ‘turning off’ molecules
  • monitor diffusion into the bleeched area over time (recovery) due to diffusion of bleached (so non-fluorescing) molecules out and fluorescing molecules in
  • using I(t) = 1 - mf*exp(t/τD)
  • where mf is the mobile fraction, the fraction of the molecules that can move
21
Q

Single Particle Tracking

A
  • tag molecules at low enough concentrations to be able to follow the motion of single molecules over time
  • calculate D from the observed random walk mean square distance: =2mDt
  • in real biological systems often observe anomalous diffusion
22
Q

Annomolous Diffusion

A
  • non-linear diffusion behaviour, ∝ τ^α
  • free diffusion is α=1
  • super diffusion is α>1, MSD increases faster than expected for random motion due to external energy input possibly caused by molecular motots or strong intracellular flow
  • sub diffusion is α<1, MSD increases slower than expected for random motion due to interactions with surrounding molecules possible caused by molecular crowding and confinement
23
Q

What use is the diffusion constant?

Rates

A

-looking at reaction rates between molecules:
rate = kon * [mol1] * [mol2]
-where [X] indicates the concentration of X

24
Q

What use is the diffusion constant?

Diffusion Limited Reaction

A

-assumes that every encounter leads to a reaction i.e. that rate is limited by diffusion ONLY
kon,diff = 4π (D1 + D2) (R1 + R2)

25
Q

Saffman-Delbruck Model

A
  • answers the question ‘does diffusion of bodies in the membrane scale with 1/R as proposed in the Stokes-Einstein equation for free bodies?’
  • predicted logarithmic dependence of proteins differentiation coefficient on it’s hydrodynamic radius
26
Q

Why is movement across membranes important?

A
  • vital to compartmentalisation and communication between cells
  • controlling differences in concentrations creates electrochemcial gradients crucial for electrical signalling, energy production and sensing
  • all viruses and drugs must cross the membrane in order to enter cells
27
Q

What are the four methods of entry into cells?

A

1) transmembrane diffusion (small molecules slip between the lipid molecules)
2) poration (free diffusion through the hole in the membrane)
3) ion channels/transporters (specifically mover certain molecules or open in response to stimuli)
4) vesicle trafficking (vesicle fuses to membrane then releases molecules on the other side)

28
Q

Important Ions

A
  • hydrogen - pH
  • potassium - movement and cognition
  • calcium - signalling, muscles
  • magnesium - activity of ATP, enzymes, muscles
29
Q

Anions

A

-chloride - pH, nerve impulses

30
Q

Complex Ions

A

OH-, NH4 +, SO4 2-, PO4 3-, HPO4 2- (Pi)

31
Q

Transmembrane Diffusion

Semi-permeability

A

NO
-large, uncharged polar molecules (glucose, sucroese)
-ions
YES
-small, uncharged polar molecules (H2O, ethanol, glycerol)
-gases (CO2, N2, O2)

32
Q

Hydrophobic, Hydrophilic and Amphipathic

Definition

A
  • hydrophobic - polar groups
  • hydrophillic - no polar groups
  • amphipathic - both polar and non-polar groups (e.g. lipid molecules)
33
Q

Transmembrane Diffusion

Solubility-Diffusion Model

A 
P = KD/d
P = permeability
K = oil/water partition coefficient, how much the molecule wants to sit in the membrane
D = solute's diffusion coefficient in the oil slab, how fast the molecule moves once it's in the membrane
d = membrane thickness
34
Q

Dependence of Membrane Permeability on Membrane Properties

A
  • membrane permeability also depends on membrane packing properties:
  • lipid species
  • temperature
  • cholesterol content
  • higher area per lipid results in higher permeability
35
Q

Transmembrane Diffusion

Flick’s Law Applied to Membranes

A 
J = -D dc/dx = -D (c1-c2)/d
= -D/d Δc
D = diffusion coefficient
d = membrane thickness
Δc = concentration difference across membrane
36
Q

Transmembrane Diffusion

Permeation Constant

A

J = -D/d Δc = Ps * Δc
=>
Ps = D/d

37
Q

Transmembrane Diffusion

Timescale of Leakage

A

Δc = Δco exp(-t/τ)
-where τ is the timescale of leakage:
τ = V / Ps*A

38
Q

Transmembrane Diffusion

Red Blood Cells

A
  • bioconcave disk shape

- high area to volume ratio to increase O2 concentration and interaction with the haemoglobin proteins inside

39
Q

Transmembrane Diffusion

Osmotic Pressure

A

-derived based on Gibbs free energy taking into account water free energy and mixing entropy

40
Q

Osmotic Pressure Equation

A 
Δp = Ns/V * kb * T
Ns = number of molecules
V = volume
T = temperature
kb = Boltzmann constant
41
Q

High Salt Concentration to Preserve Food

A
  • salt causes a hypertonic environment and plasmolysis (shrinkage)
  • imperfect method as some bacteria are halophilic -> can thrive in a high salt environment
  • certain membrane proteins can open in response to protein allowing rapid flow of molecules in/out of cell
42
Q

Ways to Deform a Membrane

A
  • 4 ways:
  • -stretch (e.g. pressure)
  • -bend (e.g. creating new vesicles)
  • -expand
  • -shear
  • each has its own eleastic response that depends linearly on the extent of deformation
43
Q

Membrane Mechanics

Free Energy Due to Stretching

A 
Fstretch = Ka/2 ∫ (Δa/a)² dA
Ka = area expansion modulus
44
Q

Membrane Mechanics

Surface Tension

A

λ = Ka (Δa/a)
-surface tension is isotropic, a force per unit length
Ka = area expansion modulus

45
Q

Membrane Mechanics

Young-Laplace Equation for Spherical and Non-Spherical Geometries

A

-spherical:
λ = RΔp/2
-non-spherical
Δp = λ [1/R1 + 1/R2]

46
Q

Membrane Mechanics

Rupture

A

-lipid bilayers rupture at 1-25mN/m

47
Q

Membrane Trafficking

A
  • transport of materials can be facilitated by lipid vesicle fusion to bring molecules into cells (endocytosis) or out of cells (exocytosis)
  • viruses can exploit these mechanics to bring genetic information into the cell to replicate and spread
  • used for communication between cells (e.g. nerve cells) by transport of communication molecules (e.g. neurotransmitters)
48
Q

Membrane Trafficking

Energy Cost

A

-use the free energy of bending equation:
Fbend = Kb/2 ∫ (Δa/a)² dA
= Ka/2 (Δa/a)² 4πR²
= 8πKb
-so energy cost is independent of vesicle radius!
-there are also proteins which aid in this process as the energy cost is generally too high for spontaneous formation

49
Q

Viral Entry Mechanisms

A
  • membrane fusion - virus membrane fuses with host membrane to release virus cell contents into host cell
  • endocytosis (without membrane fusion) virus enters cell with its own membrane intact
  • injection via loaded spring

PHYS5530M Physics of Biological Systems (12 decks)

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