Untangling the Mechanics of Entangled Biopolymers

Transcription

1 Untangling the Mechanics of Entangled Biopolymers Rae M. Robertson-Anderson Physics Department University of San Diego students/postdocs: Cole Chapman, PhD Tobias Falzone, PhD Stephanie Gorczyca, USD 16 Savanna Blair, USD 16 Kent Lee, B.A. USD 13 Funding: NSF CAREER Award AFOSR Young Investigator Award

2 Soft Squishy Matter is amazing, complex & all around us Biology Cosmetics Fascinating, multifunctional viscoelastic properties coatings Safety adhesives Comprised of polymers What s happening on a molecular level to give rise to such dynamic, complex behavior? Macroscopic Viscoelasticity Entangled Polymers Molecular-level Dynamics & Interactions

3 Biopolymers are highly versatile and tunable DNA Actin 1 mm Random Coil Conformation Persistence Length: l p =50 nm Typical lengths: 5 20 mm Extended Contour Persistence Length: l p = 17 mm Typical length: 5 20 mm Replication controls length Enzymes control topology Polymerization controls length Crosslinking proteins control actin network architecture Ring Linear

4 Biological cells are crowded with a wide variety of biopolymers Nucleic Acids 1 mm Cytoskeleton filaments Biopolymers make up ~20-40% of cell volume Crowding plays important roles in: Small Folded Proteins diffusion Binding rates Persistence Length: ~5 nm Typical length: mm Folding

5 We can track single biopolymers & measure intermolecular forces Fluorescence Microscopy & Particle Tracking Optical Tweezers Microrheology

6 We investigate molecular mechanics of crowded and entangled DNA and Actin Diffusion & Conformation of Crowded Linear & Ring DNA Nonlinear Micro-viscoelasticity of entangled DNA Mapping Deformations of Entangled Actin Filaments Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015) Chapman, Robertson-Anderson; Physical Review Letters (2014) Falzone, et al; Soft Matter (2015); MacroLetters (2015)

7 We investigate molecular mechanics of crowded and entangled DNA and Actin Diffusion & Conformation of Crowded Linear & Ring DNA Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)

8 We track single DNA molecules to directly measure molecular dynamics Slope = 2D COM R G <( x) 2 > = 2Dt Labeled DNA unlabeled crowders Minor axis (R min ) Track Center of Mass of DNA Calculate Diffusion Coefficient Track Axes lengths of diffusing DNA Quantify conformational shape and size Major axis (R max )

9 We track linear & ring DNA in dextran solutions that mimic cellular crowding Slope = 2D 10 kda dextran 500 kda dextran 115 kbp Linear DNA 115 kbp Ring DNA <( x) 2 > = 2Dt Track Center of Mass of DNA Calculate Diffusion Coefficient dextran 10% 40% concentration Track Axes lengths of diffusing DNA Quantify conformational shape and size

10 Crowded DNA universally diffuses faster than classically expected DNA diffusion in dextran solutions Short DNA Long DNA Crowders hinder linear and ring DNA mobility equally small dextran large dextran Crowder size plays principle role in diffusion reduction Classical Stokes-Einstein diffusion: D = k B T/6phR DNA mobility reduction is independent of DNA topology Mobility decreases less than classically expected from increased viscosity Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)

11 Universal scaling of DNA mobility is driven solely by reduced solution volume DNA diffusion in dextran solutions Short DNA Long DNA small dextran large dextran DNA mobility reduction is independent of DNA topology Mobility decreases less than classically expected from increased viscosity Universal mobility reduction scales exponentially with crowder volume fraction

12 Crowding induces topology-dependent changes in DNA conformation Distribution of DNA Conformations Crowder Volume fraction F C Minor axis (R min ) Major axis (R max ) Ring DNA compacts Dilute Ring Random Coil Linear DNA R max increases Crowded Ring Coil compaction Compacted ring DNA is ~47% of random coil volume Do linear chains swell or elongate? Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)

13 Crowded Ring DNA compacts while linear DNA elongates Distribution of DNA Conformations Crowder Volume fraction F C Minor axis (R min ) Major axis (R max ) Compacted rings remain spherical Linear DNA elongates as crowding increases Compacted ring DNA is ~47% of random coil volume Do linear chains swell or elongate? Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)

14 Elongated and compacted conformations are smaller than random coils Distribution of DNA Conformations Crowder Volume fraction F C Minor axis (R min ) Major axis (R max ) Compacted rings remain spherical Linear DNA elongates as crowding increases Compacted ring DNA is ~47% of random coil volume Elongated linear DNA is ~66% of random coil volume Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)

15 Elongated and compacted conformations are smaller than random coils Dilute Linear DNA Random Coil Crowder Volume fraction F C Minor axis (R min ) Major axis (R max ) Crowded Linear DNA Coil Elongation Linear DNA elongates as crowding increases Compacted ring DNA is ~47% of random coil volume Elongated linear DNA is ~66% of random coil volume Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)

16 Crowder entropy maximization drives DNA to elongate or compact to facilitate diffusion Dilute Ring DNA Crowded Ring DNA Random Coil Dilute Linear DNA Coil compaction Crowded Linear DNA Random Coil Coil Elongation Crowding forces DNA into lower entropy state to maximize entropy of crowders Smaller volume DNA states can diffuse faster through viscous crowded environment

17 We investigate molecular mechanics of crowded and entangled DNA and Actin Nonlinear Micro-viscoelasticity of entangled DNA Chapman, Robertson-Anderson; Physical Review Letters (2014)

18 The response of entangled polymers to large deformations is complex and not well understood Small strain amplitudes = linear viscoelastic response Large strain amplitudes & rates = nonlinear viscoelastic response No disruption of entanglements No chain stretching Classical tube theory cannot explain bulk experimental data Classical tube theory describes data well New proposed theories remain untested

19 We measure the molecular-level DNA response to large strains 2) Pull bead 30 mm through DNA 2) Measure force DNA exerts 1) Trap bead 4) Release bead from trap 4) Track bead recoil 3) Hold bead in trap for fixed time after strain Chapman, Robertson-Anderson; Physical Review Letters (2014)

20 We measure the molecular-level DNA response to large strains 2) Pull bead 30 mm through DNA 2) Measure force DNA exerts 10 Pulling rates: ~3 126x DNA disentanglement rate Wiessenberg No. (Wi) = DNA concentrations: ~0.5 2x entanglement concentration Chapman, Robertson-Anderson; Physical Review Letters (2014)

21 Force DNA exerts DNA stiffness The local DNA response displays key nonlinear features explained by non-classical entanglements Stress Stiffening Stress Softening Viscous behavior Nonlinear viscosity thinning for Wi >20 Linear Nonlinear Elastic Yielding Strain Wi > 20: Nonlinear tube softening entanglement loss Strain (pull) distance Pulling Rate Chapman, Robertson-Anderson; Physical Review Letters (2014)

22 Free motion of bead following strain characterizes stored entanglement elasticity Bead Recoil distance vs. time 3) Hold bead in trap for fixed time after strain 4) Release bead from trap 4) Track bead recoil Chapman, Robertson-Anderson; Physical Review Letters (2014)

23 Recoil shows non-classical tube dilation in agreement with recent nonlinear theory Bead Recoil distance vs. time Maximum Recoil distance vs Strain Rate Linear Nonlinear Exponential recoil to maximum recoil distance Recoil distance comparable to Entanglement tube diameter Strain-induced rate-dependent tube dilation Tube potential directly coupled to external stress Chapman, Robertson-Anderson; Physical Review Letters (2014)

24 Recoil decay rate shows crossover to non-classical entanglement tube healing and relaxation Recoil Decay Rate Wi < 20 Single classical tube relaxation 1. fast tube retraction Linear Nonlinear 2. Classical tube relaxation 2. Tube healing to equilibrium size Tube dilates with increasing strain rate Post-Strain Wait Time Multimode tube relaxation and power-law tube healing Chapman, Robertson-Anderson; Physical Review Letters (2014)

25 We investigate molecular mechanics of crowded and entangled DNA and Actin Mapping Deformations of Entangled Actin Filaments Falzone, et al; Soft Matter (2015); MacroLetters (2015)

26 We track actin filament deformations induced by microscale strains Discretely label segments along entangled actin filaments Track segment displacements during and following microscale strain Falzone, et al; Soft Matter (2015); MacroLetters (2015)

27 We track actin filament deformations induced by microscale strains Discretely label segments along entangled actin filaments Track segment displacements during and following microscale strain

28 We map filament deformations throughout the network out to mesoscopic length scales Quantify displacement dependence on distance from strain path Track segment displacements during and following microscale strain

29 We couple microscale stress response to induced deformations of actin filaments Filament x-displacement (um) Quantify displacement dependence on distance from strain path Measure force filaments exert to resist strain Force actin exerts (pn)

30 We link discrete filament displacements and microscale forces to mesoscale network deformations Filament x-displacement (um) What macromolecular deformations lead to the resistive network force response? How do induced deformations & stress propagate through the network? Force actin exerts (pn)

31 Elastic force response yields to dissipation at rate-dependent distances Relative resistive force actin exerts Elastic response yielding point increases with strain rate Falzone, et al; Soft Matter (2015); MacroLetters (2015)

32 The disentanglement time controls dissipative yielding of entangled actin Relative resistive force actin exerts Elastic response yielding point increases with strain rate slower than t ent faster than t ent Yield time theoretical Disentanglement time t ent Entangled actin elasticity yields to dissipation when individual entanglements can relax Falzone, et al; Soft Matter (2015); MacroLetters (2015)

33 Unexpected stress-stiffening of entanglements suggests strain-induced crosslinking Relative actin response stiffness How do entanglements deform to produce stiffening response? slower than t ent faster than t ent Linear nonlinear nonlinear stress-stiffening only predicted/measured for crosslinked actin networks Can microscale stiffening lead to macroscopic softening? Falzone, et al; Soft Matter (2015); MacroLetters (2015)

34 We map the propagation of filament deformations throughout the network x max x rec 0.3t ent 1.7t ent 3.3t ent Falzone, et al; Soft Matter (2015); MacroLetters (2015)

35 Stress-stiffening is coupled with long-range strain propagation & effective crosslinking x max x rec 0.3t ent 3.3t ent 1.7t ent fluid-like deformations exponentially die out ~persistence length from bead path Rigid entanglement deformations propagate out to several persistence lengths Long-range linear dissipation of deformations: macroscale signature of crosslinked networks Falzone, et al; Soft Matter (2015); MacroLetters (2015)

36 Fractional recovery of entanglement deformations quantifies elasticity of response Fractional Recovery: f rec = x rec/ /x max x max x rec 3.3t ent 1.7t ent 0.3t ent 0.3t ent 3.3t ent 1.7t ent fluid-like deformations exponentially die out ~persistence length from bead path Rigid entanglement deformations propagate out to several persistence lengths Long-range linear dissipation of deformations: macroscale signature of crosslinked networks Falzone, et al; Soft Matter (2015); MacroLetters (2015)

37 Actin persistence length controls spatial crossover to continuum network mechanics Fractional Recovery: f rec = x rec/ /x max All deformations beyond persistence length from strain display self-averaging behavior 3.3t ent 1.7t ent Discrete entanglement segments are mechanically linked by the persistence length of semiflexible actin filaments 0.3t ent 0.3t ent 3.3t ent 1.7t ent Many entanglements span ~17 um persistence length Mesoscale spatial crossover to continuum mechanics unique to semiflexible polymers Falzone, et al; Soft Matter (2015); MacroLetters (2015)

38 Recovery mechanics display nonclassical tube dilation near strain path Mechanics following strain Resistive force relaxation Classical Exponential relaxation Deformation recovery 3.3t ent 0.3t ent 1.7t ent Nonclassical Power-law Relaxation Force and deformation recovery display entanglement tube dilation near strain Dilated entanglements exponentially contract to classical size far from strain Discrete hierarchical continuum Exponential deformation recovery rates Tube dilation Classical tube dynamics Falzone, et al; Soft Matter (2015); MacroLetters (2015)

39 Mesoscale continuum mechanics suppress microscale nonlinearity Mechanics following strain Resistive force relaxation Classical Exponential relaxation Deformation recovery 3.3t ent 0.3t ent 1.7t ent Recovery/elasticity persists out to ~2l p Nonclassical Power-law Relaxation Force and deformation recovery display entanglement tube dilation near strain Dilated entanglements exponentially contract to classical size far from strain Microscale nonlinearity suppressed to linear response beyond persistence length Discrete hierarchical continuum Exponential deformation recovery rates Tube dilation Classical tube dynamics Falzone, et al; Soft Matter (2015); MacroLetters (2015)

40 Molecular-level experiments reveal complex biopolymer dynamics in entangled & crowded systems Diffusion & Conformation of Crowded Linear & Ring DNA Ring DNA Linear DNA Nonlinear Micro-viscoelasticity of entangled DNA Falzone, et al; Soft Matter (2015); MacroLetters (2015) Mapping Deformations of Entangled Actin Filaments Crowding-induced compaction & elongation facilitates DNA diffusion Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015) Crossover to nonlinear viscoelasticity is driven by nonclassical entanglements Chapman, Robertson-Anderson; Physical Review Letters (2014) Persistence length controls crossover to continuum network mechanics Nonlinear strains induce crosslinking of entanglements

41 Undergraduates can do amazing things! (UCSD grad students are pretty good too) Diffusion & Conformation of Crowded Linear & Ring DNA Nonlinear Micro-viscoelasticity of entangled DNA Mapping Deformations of Entangled Actin Filaments Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015) Chapman, Robertson-Anderson; Physical Review Letters (2014) Falzone, et al; Soft Matter (2015); MacroLetters (2015)

42 Displacement vector maps display osmotically-driven filament motion near strain path 0.3t ent osmotic restoring force leads to: -trailing-edge attraction, leading-edge repulsion -trailing-edge wake at high strain rates 3.3t ent Falzone, et al; Soft Matter (2015); MacroLetters (2015)

43 Nonaffine filament deformations show strain-induced crosslinking of entanglements 0.3t ent osmotic restoring force leads to: -trailing-edge attraction, leading-edge repulsion -trailing-edge wake at high strain rates affine (x) nonaffine (y) Power-law scaling of nonaffinity: signature of crosslinked networks Strains faster than t ent induce crosslinking of entanglements 3.3t ent Strain-induced suppression of nonaffine modes Falzone, et al; Soft Matter (2015); MacroLetters (2015)

44 Compact rings and elongated linear chains fluctuate at same rate when crowded Chapman, et al; Biophysical Journal (2015) Gorczyca, et al.; Soft Matter (2015)