DNA as a Polymer Flashcards
Degree of Polymerisation
Definition
-number of monomers, N
Total Mass of Population
Definition
M = N*m_mon
-where m_mon is the mass of a monomer unit
Homopolymer/Heteropolymer
Definition
- a homopolymer is made up of the same monomer
- a heteropolymer is in a random or block structure
Polymer Flexibility
- coil or rod like
- this is length scale dependent, characterised by the persistance length
Polymer Isomerisation
- isotactic, chemical groups on the same side
- syndiotactic, chemical groups on opposite sides
- atactic, chemical groups randomly distributed
Polymer Topology
- linear
- ring/circular
- branched
Polymer - Molecular Conformations
- atoms and molecules in a thermal bath follow random walks
- for a distribution of ensemble isotropic chains, every angle between steps is equally probable
- because each angle is equally probable, over a large number of steps, the ensemble average is zero so take the means square instead
Polymers - Ideal Chain Model
-assume fixed bond length: l = |ri| = |rj| ri . rj = l²cos(θij) -mean square distance : = l²ΣΣ -summed over I and j from 1 to n
Freely Jointed Chain Model
-no correlations between any θij’ and θij are allowed, so:
= 0 for I not equal j
-only N non-zero terms in the double sum since cos(θij)=1 only for I=j
=> = Nl²
-individual chain distance away from start point scales with sqrt(N) steps of step length l
Freely Jointed Chain Model
Real Chains
-as there are no angular restrictions from one bond to the next, the model allows the chain to cross or go through itself which obviously isn’t possible for a real chain
-this leads to the concept of excluded volume, the chain can’t move into the space already occupied by the chain
-for real chains:
not equal 0
Flory-Characteristic
-even after removing crossing over, after many many bonds, the pointing vector will be completely decorrelated from the final vector in the chain:
Ci = Σ
-summed over j from 1 to n
= CnNl²
-where N is the number of bonds and l is the bond length
-Cn is the Flory characteristic ratio, the average of all Ci
Contour Length
-the total length of the polymer
L = Nl
Freely Rotating Chain Model
Description
- bond lengths l and bond angles θ are both fixed
- but chain segment can take any torsional angle with no correlations:
- π < φi ≤ π
- the only correlation between bond vectors is that transmitted down the chain by the previous bond vectors component lcosθ
Persistence Length
-the range over which correlations between bond vectors has decayed
Number of Bonds in a Persistence Length
sp = 1 / -ln(cosθ)
Freely Rotating Chain Model
Mean Square Distance
-mean square distance is now also modulated by the fixed angle between bond vectors:
= nl² [1+cosθ]/[1-cosθ]
-where
C∞ = [1+cosθ]/[1-cosθ]
Worm Like Chain Model
Description
-used for very stiff polymers, such as double stranded DNA
-as the polymer is stiff, θ is very small, so we can expand:
cosθ ≈ 1 - θ²/2
-since θ is small, the correlation length is longer so sp is larger
Worm Like Chain Model
sp
ln(cosθ) ≈ - θ²/2
=>
sp = - 1/ln(cosθ) ≈ 2/θ²
Worm Like Chain Model
Persistane Length
lp = sp*l = 2l/θ²
Worm Like Chain Model
Flory Ratio
C∞ ≈ 4/θ²
Worm Like Chain Model
Limits
-two limits can be taken from the WLC model:
1) ideal chain limit for very long chains:
≈ 2lpl, L»lp, perfect coil
2) rod like limit for very short chains:
≈ L², L<
What is a typical persistence length for double stranded DNA?
~50nm
-this is quite long as double stranded DNA is a double helix making it a relatively stiff polymer
Suitable Models for Nucleic Acid Polymers
RNA and ssDNA
- RNA and ssDNA may be best modelled by FJC or FRC models but we can also use a WLC model with bond length l of nucleotide repeat along the chain
- each nucleotide acts independently ad can rotate around the sugar phosphate backbone single bond
Suitable Models for Nucleic Acid Polymers
dsDNA
- dsDNA is well modelled by the WLC model with lp~50nm
- the double helix makes dsDNA more rigid, the backbone is able to curve but is more or less fixed in place
