Mechanical properties of DNA under twisting Why important – biology: curved/bent DNA important in packing into nuclei, into viruses, in regulation of transcription, various enzymes bend/twist DNA during replication, transcription, recombination technology: important for using DNA as tool to pull, twist objects; to study how various enzymes that act on DNA work; (next class)

What we’ll cover: low torque limit, twisting compliance supercoils, topological changes high torque – structural changes (P, L forms) coupling between twisting and stretching

Nature 424, 338 (2003) Demonstrates some of the versatility of laser trap technology

Experimental system DNA made by pcr and restr. enz. cutting + ligation; ss nick allows bottom part to swivel apply torque keep const. tension observe 

Attaching small SA-coated bead to biotinylated DNA stretched between larger beads

Torque inferred from rotational velocity  =   = 14  r 3  (rotational equiv. of Stokes’ law) 0.7  m bead0.9  m bead

Low torque regime,  = (C/L  0   C = 410 +/- 30 pN nm 2

Caveat on units torque = r x F, units = [Nm], same as energy But energy = torque x angle, angle “unitless” in radians Less confusing if we refer to energy done by torque as Newton-meter-radians Easy to lose track of radians in equations because units often go unmentioned

(C/L)  2  k b T, C = 440 +/- 40 pN nm 2 Independent measure of C in absence of torque based on equipartition theorem No extra twists, no flow, let bead drift via Brownian motion

C doesn’t change (in linear region) for + or - twist But at  crit, torque abruptly stops increasing/ decreasing with more twists What’s going on?

Interpretation: At  crit, DNA undergoes phase change (B->P), more twisting converts more B-form to P-form,  constant until all DNA converted. At  crit, twisting work like latent heat of melting, converts ice to water without inc. temp.; phase co-existence acts as torque clamp.

Coupling between stretching and twisting Imposing F>65pN converts B DNA to S DNA. S DNA has longer rise/bp but also fewer twists/bp, so DNA unwinds as it extends. On reducing F to 0, DNA collapses to massively under-wound (? partially melted) state, then rewinds to form B DNA. B-S phase equilibrium acts a Force-Torque converter

Hypothesized phase diagram Circles = measured critical points scP = supercoiled P

Biological applications of this technology Study mechanisms of protein “machines” that act on DNA (pull, twist, wrap, recombine) Example – topoisomerases, enzymes that change topological form of DNA strands, major targets of antibiotics and cancer drugs Type 1 topoisomerases nick and reseal 1 strand of dsDNA, relaxing over- or under-wound segments Type 2 topoisomerases cut and religate both strands of dsDNA, untangling “concatenated” DNAs

NS F Experimental setup used to study topo I Primer for next weeks class – see biophysics/practical_handouts/magnetictweezers.pdf

Replication of circular bacterial chromosome sometimes -> entangled daughter strands newly synthesized “daughter” strands Role of topo 2 – untangling interlocked DNAs “Catanated DNA”

Type 2 topoisomerase can disentangle by cutting one strand, passing second strand through cut, and religating

Many enzymes/nanoscale motors can be studied using DNA pulling and twisting technology – for example: topoisomerases (class 7) ribosomes moving on RNA (class 8) dynamically assembling protein polymers (class 9) proteins that move along such polymers (class 10)

Applications in nanotechnology Knowledge of DNA elastic properties important for constructing nano objects with DNA ? constant torque wind-up motors ? force-torque converters (Your creative application goes here)

Main points: For small forces (  pN), DNA acts like entropic spring FJC model -> WLC model for forces > 65pN, DNA undergoes structural change with constant force, 2-phase equilibrium For small torques, DNA acts like torsional spring for large torques, DNA undergoes structural changes with constant torque, 2-phase equilibia Strong forces assoc with structural changes couple elongating and twisting -> force-torque converter

Methods developed in these studies – attaching DNA ends to beads and flat surfaces paramagnetic beads and magnetic tweezers laser trap allow remarkable manipulation of individual macromolecules, observation of their response to pN forces and torques, and their ability to effect pN forces and move sub-  m distances will discuss their application in several future classes