Friction and torque govern the relaxation of DNA

supercoils by eukaryotic topoisomerase IB

…By Daniel A. Koster, Vincent Croquette, Cees Dekker, Stewart

Shuman & Nynke H. Dekker

Topoisomerases in general

• Enzymes that binds to DNA molecules (at specific sequences) and relieves them of torsional strain, i. e. removal of supercoils

• Supercoil removal happens through a cleavage-religation cycle

• Two types: topI binds to ssDNA

topII binds to dsDNA

Basic properties of topIB

• Has a clamp-like structure, enveloping the DNA molecule

• Removes supercoils by a swivel mechanism contrary to the strand-passage mechanism seen in topIA and topII

Cleavage-religation procedure

• Transesterification results in formation of a DNA-(3’-phosphotyrosyl)-enzyme intermediate and a free 5’-OH DNA strand

• Supercoils are relaxed through the rotation of the 5’-end around the fixed second DNA strand

• The 5’-strand engages the DNA-enzyme intermediate; enzyme dissociates

Cleavage-religation procedure

• The enzyme enveloping the DNA leads to friction and thereby a hindered or “controlled” rotation of the 5’-strand takes place

Goals

• To examine the action of topIB on a single molecule level by using magnetic tweezers

• To present a model that describes the effect of friction and torque on the activity of topIB, and to compare it with experimental results

Experimental setup

• dsDNA from bacteriophage λ is anchored between a glass plate and a paramagnetic bead

• By application of a magnetic field the DNA molecule is subject to an extension force

Experimental procedure

• Rotation of the magnetic field results in a growing torque on the DNA

• At a critical value Γc the torque saturates and the DNA starts to form supercoils, thereby reducing the extension of the molecule

Experimental procedure

• Linking number

Lk = Wr + Tw• Degree of supercoiling σ = (Lk –Lk0 ) ∕ Lk0

with Lk0 the linking number of uncontrained, linear DNA

(Lk0 = Tw0; # of helical turns)

Experimental procedure

• By addition of vaccinia topIB, the DNA extension increases in a discrete, step-wise manner

• Each step signifies removal of supercoils through a cleavage/religation cycle, and thereby a change in linking number, ∆Lk

The distribution of ∆Lk

• P(∆Lk) ≈ exp(- ∆Lk /<∆Lk>); <∆Lk> is the mean change in linking number or mean stepsize.

Propability p for religation at each rotation → discrete probability function P(∆Lk) = p(1 – p)^ (∆Lk-1) with <∆Lk> ≡ 1/p. Turns into the expression above in the continuum limit

Control measurement

• For nicking enzyme, <∆Lk> = # of supercoils initially applied (insert).

• Unable to religate DNA → DNA completely relaxed at once

The dependence of <∆Lk> on stretching force

• The mean stepsize <∆Lk> is found to increase with stretching force F

• The probability for religation per rotation decreases with F (insert)

• Inconsistent with a strand-passage mechanism - favours a swivel mechanism

The dependence of <∆Lk> on stretching force

• To be continued…

Velocity of DNA extension can be resolved in real-time

• DNA extension as a function of time is resolved for a single cleavage-religation step, and by fitting to a linear function the extension velocity is obtained

• The extension velocity is a measure of the rate at which the 5’-DNA rotates inside the enzyme cavity as supercoils are released

Distribution of DNA extension velocity at fixed F (0.2 pN)

• Dark red triangles: human topIB. <v> = 4.1 ± 0.2 μm/s• Red diamonds: wild-type vaccinia topIB. <v> = 6.7 ± 0.2 μm/s• Beige circles: topIB Y70A mutant. <v> = 8.9 ± 0.6 μm/s• Blue triangles: nicking enzyme. <v> = 10.5 ± 0.2 μm/s• Green squares: mix of topIB Y274F mutant & nicking enzyme.

<v>=10.5 ± 0.2 μm/s

Distribution of DNA extension velocity at fixed F (0.2 pN)

• Human topIB and vaccinia topIB slows down the DNA rotation rate compared to the unhindered rotation observed for nicking enzyme

• Human topIB (O-shaped clamp) convolutes the DNA molecule even more than vaccinia topIB (C-shaped clamp) → slower rotation rate

Distribution of DNA extension velocity at fixed F (0.2 pN)

• Y70A topIB mutant is missing a tyrosine side chain normally situated at the inside of the cavity → less friction → higher rotation rate

• Y274F lacks the ability of transesterification → binds to DNA, but cannot cleave; no change in rotation rate observed for nicking enzyme when mixed with Y274F

Distribution of DNA extension velocity at fixed F (0.2 pN)

• These measurements indicate that friction plays a role in the topIB relaxation mechanism

A model for topIB activity

1. As we have just seen, supercoil removal by topIB is hindered by friction inside the enzyme cavity

2. The uncoiling is driven by the mechanically applied torque, Γc

3. Within each 2π rotation of the DNA, there is one position at which religation happens with significant probability, namely in close proximity to the fixed 3’-DNA strand

A model for topIB activity

• Schematic description of the model: the dependence of ∆G on rotation angle θ

• Rotation speed not smooth, perhaps stemming from the varying cross-sectional diameter of the DNA molecule during the rotation cycle (from 2 nm at θ = 0 to approx. 4 nm at θ = 180 degrees

A model for topIB activity

• Each energy barrier in the landscape is described by an Arrhenius behavior k ≈ exp(-∆G/kBT)

• The torque is modelled by tilting the energy landscape by - Γcθ, thereby decreasing ∆G by an amount Γcδθ. We now have k ≈ exp(-(∆G-Γcδθ)/kBT)

A model for topIB activity

• The force-dependence of the torque is given by Γc(F) = √2kBTξF (torsional directed walk model) with ξ the persistence length of dsDNA (53 ± 2 nm)

• The regions of possible religation are shown as green bars. Religation probability: p = kr / k’

A model for topIB activity

• Religation probability: p = kr / k’ with kr the rate constant for establishing a covalent bond and Tres ≡ 1 / k’ the residence time at the religation location

A model for topIB activity

• Putting it all together we deduce

p(F) = exp(- δθ√2kBTξF/kBT) or

<∆Lk(F)> = <∆Lk>F=0exp(δθ√2kBTξF/kBT)

Results

• The expressions for p(F) and <∆Lk(F)> are fitted to the data and an estimate of δθ and <∆Lk>F=0

is made

Results

• δθ = 0.23 ± 0.02 radians (≈13 degrees)• <∆Lk>F=0 = 19.3 ± 2.3 (positive) supercoils per cleavage-

religation cycle• Bulk measurements: <∆Lk>F=0 = 5 ± 1.5 supercoils per

cycle (performed on plasmids containing 15 ± 2 supercoils and using ensemble-averaged rate constants)

The End