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 Γ c the torque saturates and the DNA starts to form supercoils, thereby reducing the extension of the molecule

Experimental procedure Linking number L k = Wr + Tw Degree of supercoiling σ = (L k –L k0 ) ∕ L k0 with L k0 the linking number of uncontrained, linear DNA (L k0 = Tw 0 ; # 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, ∆L k

The distribution of ∆L k P(∆L k ) ≈ exp(- ∆L k / ); is the mean change in linking number or mean stepsize. Propability p for religation at each rotation → discrete probability function P(∆L k ) = p(1 – p)^ (∆L k -1) with ≡ 1/p. Turns into the expression above in the continuum limit

Control measurement For nicking enzyme, = # of supercoils initially applied (insert). Unable to religate DNA → DNA completely relaxed at once

The dependence of on stretching force The mean stepsize 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 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. = 4.1 ± 0.2 μm/s Red diamonds: wild-type vaccinia topIB. = 6.7 ± 0.2 μm/s Beige circles: topIB Y70A mutant. = 8.9 ± 0.6 μm/s Blue triangles: nicking enzyme. = 10.5 ± 0.2 μm/s Green squares: mix of topIB Y274F mutant & nicking enzyme. =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, Γ c 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/k B T) The torque is modelled by tilting the energy landscape by - Γ c θ, thereby decreasing ∆G by an amount Γ c δθ. We now have k ≈ exp(-(∆G-Γ c δθ)/k B T)

A model for topIB activity The force-dependence of the torque is given by Γ c (F) = √2k B TξF (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 = k r / k’

A model for topIB activity Religation probability: p = k r / k’ with k r the rate constant for establishing a covalent bond and T res ≡ 1 / k’ the residence time at the religation location

A model for topIB activity Putting it all together we deduce p(F) = exp(- δθ√2k B TξF/k B T) or = F=0 exp(δθ√2k B TξF/k B T)

Results The expressions for p(F) and are fitted to the data and an estimate of δθ and F=0 is made

Results δθ = 0.23 ± 0.02 radians (≈13 degrees) F=0 = 19.3 ± 2.3 (positive) supercoils per cleavage- religation cycle Bulk measurements: F=0 = 5 ± 1.5 supercoils per cycle (performed on plasmids containing 15 ± 2 supercoils and using ensemble-averaged rate constants)

The End