Lecture 11' Structural Transitions in Nucleic Acids I

8/14/2019 Lecture 11' Structural Transitions in Nucleic Acids I

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Lecture 10 Structural Transitions in

Polynucleic Acids I


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Introduction

Structural Transitions in Nucleic Acids can also be modeled using statistical thermodynamics.

We will generally adopt the Zipper Model:

in which multiple nucleation events are unlikely

so that conformations contain exactly 1 helix-island.

Model has 2 parameters:

propagation parameter (s):

describes the energetic favorability/residue of the transition:

s = exp[-Go

res/RT].

nucleation parameter ():

describes the cooperativity of the transition:

due to extra energy required to form the junction.

here, 0 <


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Nucleic Acid Transitions

Nucleic Acids participate in many interestingtransitions:

several analogous to polypeptide coil-helix and helix-coil

transitions:

annealing of single-stranded DNAs (ssDNAs) to form double-stranded (ds) B-DNA helices.

and the reverse-process (DNA melting).

folding of ssRNA to form double-stranded A-helical regions.

others involve transitions b/w two well-defined helices:

the B-DNA to A-DNA transition. the B-DNA to Z-DNA transition.

within linear and circular DNA.

First, we consider dsDNA melting/annealing.


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DNA Melting and Annealing Curves

Both the DNA melting and annealing transitions arecharacterized by a midpoint temperature: where the fraction of single-stranded (ss) DNAs = .

Tm = melting temperature.

Ta = annealing temperature.

these curves are often distinct: so that Tm > Ta.

particularly for long DNAs and fast cooling rates.

this is called hysteresis.

Hysteresis expresses structuraldifferences: between -melted DNAs and -annealed DNAs.

differences in kinetic mechanism.

as well as the degree of irreversibility in melting.

We first consider the DNA melting process modeled as a reverse transition, using the Zipper model.


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DNA Melting: The Zipper Model

Simplest case: homo-duplex melting: i.e., dsDNA consisting of 1 kind of base-pair.

Similar to the polypeptide helix-coil transition, although the molecular details differ.

We apply the Zipper model: where we neglect strand-separation.

forward transition: coil to helix (annealing).

melting treated as the reverse transition: from a fully helical state, H.

in which all base-pairs adopt a helical state, h.

i.e., H = hhhhhh to a fully melted state, C.

in which all base-pairs adopt a coil state, c.

i.e., C = cccccc

Application requires definition of:

a nucleation parameter, . a propagation parameter, s.


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Defining the Propagation Parameter

The parameter s defined for the forward transition: i.e., for the conversion from coil (c) to helix (h).

s estimated by the Gibbs Factor:

s = exp[-Gcho/RT]

where Gcho = Goh-Goc is the free energy change:

for the conversion of 1 residue from coil to helix.

note: reference state is the all-coil state, C.

i.e., the state of 0 free energy, and weight 1.

Definition of s requires: consideration of the stabilizing energies in DNA. determination of the free energy change,

Gcho

= Hcho

- T Scho

accompanying the transition of a residue from coil to helix.


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Helix Stabilized by Stacking

DNA and RNA melting typically conceptualized: in terms of H-bond breakage:

allowing strand separationhowever:

Nucleic acid helices stabilized primarily by stacking:

Stacking b/w H-bonded base-pairs: hides hydrophobic rings from water;

aligns ring dipole moments;

maximizes ring VdW interactions;

very favorable ( ~ -8.4 kcal/mol).

In contrast, H-bonding b/w bases:

only marginally (a little) favorable, in Aq. solution.

Transition from c to h thus Exothermic:

stacking of a base-pair releases heat

Hcho

= Hstacko

< 0.


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Temperature-Dependence of s

Since Gcho

is Temperature-dependent.

s will also depend on T.

An experimentally useful expression of this dependence

expressed by our Vant Hoff relation:

Since Ho

ch < 0, we expect: for T < Tm, s > 1:

propagation of a nucleated helix region favorable.

for T > Tm, s < 1:

propagation of a nucleated helix region inhibited.


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Sequence-Dependence of s

In practice, stacking Gos depend on GC

content

And will vary with specific doublet identity:

i.e., adjacent pairs of base-pairs.

We will expect the size of our propagationparameter:

s = exp[-Gcho/RT],

to increase with GC content;

Duplexes with higher GC-content:

should form more easily

and be more resistant to melting.


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Sequence-dependence of Duplex Tm

Increase in s with increasing GC content: due to increased stacking

favorability

observed experimentally by

variations in duplex Tm

.

Duplex Melting Temperature:

increases roughly linearly with

increasing GC content.

note that stacking is a very strong

interaction:

most duplexes essentially completely stacked at 25oC.

Stacking more favorable at high [Na+]:

because of decreased electrostatic repulsion

due to counterion screening of the charged backbones.


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The Nucleation Parameter,

The stacking process is cooperative: unstacking destabilizes neighboring, unmelted base-pairs.

often estimated as follows

Unstacking a single, central base-pair:

causes H-bond dissociation, with a weight change of/ = /s.

Physically, this results in the loss of 2 stacks:

1 accounted for by 1/s.

the other must be accounted for by .

Thus, the cooperativity parameter, : can be estimated by the Gibbs factor:

= exp[Go

stack/RT] = 1/s.

experiments indicate a larger penalty: ~ 10-3

-10-4

. This justifies our Zipper approximation (since


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Melting at the Middle vs. Ends

Relative favorabilities of end and middlemelting: considered by comparing total statistical

weights: initiating melting at an end:

e = 2sN-1 initiating melting in the middle:

m = (N-2)2s

N-1

relative probabilities:

Pe/Pm = e/m = 2/N.

Similar to the result obtained forpolypeptides: ends melt first for duplexes with N < 2/;

Short; high central GC-content.

middle melts first for duplexes with N > 2/; Long; low central GC-content.


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DNA Annealing

DNA Melting is kinetically simple: DNA begins as an intact, perfectly-aligned helix melting progresses from the

ends or middle.

shifted states very unlikely.

Aligned Zipper model neglects: occupancy of shifted states:

assumes perfect alignment.

conformations with internal loops.

Reasonable for modeling the melting of short DNAs.

The reverse transition is DNA Annealing kinetically much more complex

single strands may nucleate in any alignment: need not be perfectly-aligned.

thus, many other types of states may be occupied.


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Comparison with Experiment For short, quasirandom dsDNAs:

Good agreement with DNA melting curve... Aligned Zipper Model (solid line). Experimental values (circles);

Implication: A single cooperatively-melting region;

As noted by the single sigmoid;

Good agreement with annealing curve Melting strictly reversible for short DNAs.

ButNOT with fast cooling!

Fast cooling causes Hysteresis (figure) Curves distinct: indicates irreversibility.

However - limited range of validity: Not valid for longer dsDNAs:

2 or more cooperatively-melting regions: Zipper approximation fails.

Also inadequate for many short, annealing systems: e.g.: with staggered alignments/hairpin formation;

Multi-strand systems (more than 2 ssDNA species). More general model: Lecture 12.


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Transitions between Helices

The reference-state for dsDNA is a B-Helix, under physiological conditions.

however, DNA can adopt a variety of other helical structures: another slightly under-wound right-handed helix: A-DNA

helical twist of about 32.7o vs. 34.3o (B-Helix)

a left-handed helix: Z-DNA; a DNA triplex: H-DNA;

DNA cruciforms, etc

Transitions between the various helices: have been observed in both linear and circular DNAs.

Two of the interesting ones are:

the transition from B-DNA to A-DNA (this lecture),

the transition from B-DNA to Z-DNA (probably not covered)


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The B-DNA to A-DNA Transition The transition from B-DNA to A-DNA

can be induced in poly-[dG:dC] by addition of ethanol. as A-DNA is dehydrated, relative to B-DNA.

This transition can be modeled Using the familiar aligned zipper model

By applying our expression for : where is the mean fraction of base-pairs stacked in an

A-helical conformation.

The propagation parameter, s is related to the Gibbs factor:

s = exp[-Go

BA/RT] ,

here, Go

BA = Go

A - Go

B, where:

Go

B = free energy of stacking for a B-DNA base-pair doublet;

Go

A = free energy of stacking for an A-DNA base-pair doublet.

The nucleation parameter, = exp[-Go

J/RT] < 1.

G

o

J = extra energy required to form two A-B junctions.


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Comparison with Experiment

B-DNA to A-DNA transition in poly-[dG:dC]: induced by addition of ethanol.

here, discrete points illustrate experimental data.

Zipper model parameters:

Propagation parameter, s: literature standard values.

Nucleation parameter, = 0.14.

transition only slightly

cooperative

due to a modest junctionenergy :

Go

J = +5 kJ/mol.

solid line indicates :

excellent agreement.


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Conclusion

In this Lecture, we have discussed application of thesimple Zipper model:

To the various transitions of Nucleic Acids:

The DNA helix-coil transition (melting).

DNA Annealing.

The B-DNA to A-DNA transition.

which demonstrate good experimental agreement

Next lecture, we will extend our discussion of DNA

melting By relaxing our assumption of perfectly-matched DNA.

And discuss the staggered zipper model.

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Lecture 11' Structural Transitions in Nucleic Acids I