COMPLEX EFFECTS OF MOLECULAR TOPOLOGY, LENGTH AND CONCENTRATION ON MOLECULAR DYNAMICS IN ENTANGLED DNA BLENDS

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1 COMPLEX EFFECTS OF MOLECULAR TOPOLOGY, LENGTH AND CONCENTRATION ON MOLECULAR DYNAMICS IN ENTANGLED DNA BLENDS Students Cole E. Chapman Kent Lee Dean Henze Collaborators Doug Smith (UCSD) Sachin Shanbhag (FSU) Rae M. R. Anderson University of San Diego

2 STATUS QUO NEW INSIGHTS Elucidating the molecular dynamics, conformations, and interactions occurring in complex entangled biopolymer systems via novel single-molecule techniques END-OF-PHASE GOAL QUANTITATIVE IMPACT Bulk Rheology Most experimental studies on polymeric fluids are bulk studies unable to determine molecular dynamics and interactions underlying measured properties No concrete predictions for tunability Synthetic Linear Polymers theory/experiment largely developed for monodisperse linear polymers (not ideal for industry) ring polymers (valuable material properties) difficult to synthesize polymer blends not well understood DNA: ideal polymer platform replication/purification: reproducibility, exact known lengths/topologies of polymers Ring DNA Reliable feasible preparation Molecular-Level Dynamics of Ring-Linear DNA Blends Molecular diffusion of ring and linear DNA in entangled ring-linear blends: complex dependence on species fraction, wide parameter space for tunability MAIN ACHIEVEMENTS: Comprehensive molecular-level characterization of molecular diffusion in ring-linear DNA blends fluorescence microscopy, single-molecule tracking used to measure selfdiffusion of ring and linear DNA in ring-linear blends simulations mimicking experimental conditions used to determine theoretical basis for findings determined dependence of self-diffusion on fraction of linear species in blend (f L ), solution concentration, molecular length Dual-function fluorescence force-measuring dual-trap optical tweezers to probe molecular-level material response instrument has been built and calibrated Preliminary microrheology techniques/assays have been developed HOW IT WORKS: diffusion measurements: single-particle tracking of labeled purified DNA molecules via fluorescence microscopy and custom-written software tightly-focused infrared laser, optical, electronic and piezoelectric components form optical trap around fluorescence microscope Current Impact previously unknown complex dependence of linear DNA diffusion in ring-linear blends revealed theoretical basis for molecular mechanisms for tunability of material properties instrumentation development to link molecular-level deformation to induced force Planned Impact characterization of bilinear DNA blends molecular-level stress-strain relationships between deformation to induced force in DNA blends Research Goals develop novel molecular-scale stress-strain transducing and sensing technique employing fluorescence microscopy and force-measuring optical tweezers to elucidate molecular dynamics and intermolecular forces governing material properties of entangled DNA blends Connect molecular dynamics to macroscopic properties of entangled polymer systems

3 Biopolymer Dynamics to Material Properties Systems of entangled biopolymers, such as DNA: display COMPLEX and USEFUL viscoelastic properties Properties vary widely with LENGTHS and TOPOLOGIES of molecules excellent platform for NEW multifunctional, TUNABLE, dynamic MATERIALS To effectively harness intriguing bulk properties essential to elucidate molecular dynamics and interactions that give rise to them

4 Barriers to Progress Entangled biopolymer systems that exhibit the most INTRIGUING and USEFUL properties consist of BLENDS of polymers of different lengths and/or topologies theoretical and experimental PROGRESS has focused on MONODISPERSE systems of LINEAR polymers Most experiments: BULK studies underlying molecular mechanisms only inferred via theoretical predictions To effectively harness intriguing bulk properties essential to elucidate molecular dynamics and interactions that give rise to them

5 GOAL 1 GOAL 2 GOAL 3 Program Goals Measure self-diffusion coefficients for single DNA molecules in ring-linear and bilinear DNA blends using fluorescence microscopy and particle-tracking. Quantify dependence of diffusion on molecular length and topology, solution concentration, and fraction of the two species comprising the blend. Develop novel approach and instrumentation that combines optical tweezers and fluorescence microscopy to measure forces resisting displacement of single entangled DNA molecules while simultaneously imaging conformations and dynamics of individual surrounding molecules to allow for direct probing of molecular interactions, stress and strain occurring in real-time at the singlemolecule level. Apply Goal 2 technique to study molecular interactions and dynamics governing entangled ring-linear and bi-linear DNA blends to determine (1) the properties of the tube-like molecular confining field, (2) the forces resisting linear and nonlinear strains, (3) the spectrum of relaxation time constants following displacement, and (4) induced strains, conformations and dynamics of the surrounding molecules. Dependence on molecular length and topology, solution concentration, and fraction of two blend species will be studied and compared with theoretical predictions.

6 Progress towards Achieving Goals GOAL 1 COMPLETED DIFFUSION MEASUREMENTS for ring-linear DNA blends NEW: Simulations of ring-linear DNA diffusion measurements carried out to determine theoretical description of molecular dynamics Currently conducting experiments/simulations with bi-linear DNA blends GOAL 2 Dual function fluorescence force-measuring dual-trap optical tweezers HAS BEEN BUILT Biochemical assays are currently being developed for proposed method NEW: Additional microrheology measurement techniques are being developed NEW: Linear oscillatory microrheology measurements carried out for entangled linear DNA GOAL 3 Goal 2 must be completed before starting Goal 3

7 Transformational: Impact on Field Systems of entangled biopolymers, such as DNA, display complex and useful viscoelastic properties which are highly dependent on the lengths and topologies of the molecules, making these systems an excellent platform for new multifunctional, dynamic materials. To effectively harness these intriguing bulk properties, it is essential to elucidate the molecular dynamics and interactions that give rise to them. However, most experiments investigating entangled polymers have been bulk studies probing material properties, so the underlying molecular mechanisms could only be inferred via theoretical predictions that relate the two. By using DNA and novel single-molecule techniques, we can directly probe molecular dynamics, conformations and interactions, thereby directly testing theoretical predictions and elucidating the connections between the molecular and macroscopic dynamics of entangled polymer systems. As such, this research will fill a long-standing gap in knowledge regarding these highly important and poorly understood systems.

8 Theoretical Predictions: Reptation Model Many-body one body, mean field Tube radius only parameter needed to describe dynamics of entangled polymer melts Blob Theory: extension to concentrated solutions correlation blob monomer concentrated solution melt

9 Theoretical Predictions: Reptation Model Predictions about dynamical behavior of entangled polymer melts and solutions Good agreement with experiment but not exact Other dynamic mechanisms introduced to account for discrepancies e.g., Constraint Release

10 Can Circular Polymers Reptate? Circular Polymer entangled in a Linear melt: Klein, J. (1986) unpinned, linear unpinned with large loops pinned or threaded Multiple differing Theories to describe RL blends and ring polymer melts Conflicting experimental results, not universally accepted due to caveats No extension to concentrated solutions no predictions for concentration dependence of dynamics

11 DNA Replication -> homogeneous samples of exactly the same length Why DNA? Enzymes can precisely control topology supercoiled ring linear Direct visualization of single molecules Manipulation of single molecules 12 mm 45 kbp (15 mm)

12 Program Goals: Goal 1 Measure self-diffusion coefficients for single DNA molecules in ringlinear and bi-linear DNA blends using fluorescence microscopy and particle-tracking. Quantify dependence of diffusion on molecular length and topology, solution concentration, and fraction of the two species comprising the blend. Progress towards Achieving Goal 1 COMPLETED MEASUREMENTS for ring-linear DNA blends NEW: Simulations of ring-linear DNA diffusion measurements carried out to determine theoretical description of molecular dynamics Currently conducting experiments/simulations with bi-linear DNA blends

13 Label DNA with fluorescent dye Diffusion Measurements Mix with solution of unlabeled entangled linear and/or circular DNA C.M. R G Direct Observation of Brownian Motion Center of Mass of Single DNA Molecules tracked over time Einstein relation used <( x) 2 > = <( y) 2 > = 2Dt

14 Surrounding Matrix Molecules Circular Linear Diffusion in Entangled DNA Solutions Labeled Probe Molecule Linear Circular Robertson, R.M. & Smith D.E., PNAS (2007) Relative Diffusion Coefficients vs Topology Matrix topology has strong effect on diffusion 45 kbp, 1 mg/ml Strongly hindered diffusion of circles in linear matrix But with many Entanglements REPTATION is primary mode of diffusion for entangled LINEAR molecules CIRCULAR molecules CAN REPTATE (but not as well) CIRCULAR MOLECULES forced to diffuse via slow process of CONSTRAINT RELEASE

15 Surrounding Matrix Molecules Circular Linear Diffusion in Entangled DNA Solutions Labeled Probe Molecule Linear Circular Robertson, R.M. & Smith D.E., PNAS (2007) Relative Diffusion Coefficients vs Topology Matrix topology has strong effect on diffusion 45 kbp, 1 mg/ml Strongly hindered diffusion of circles in linear matrix Concentration reduced to 0.1 mg/ml Below critical entanglement Concentration Length Length reduced to 6 kbp Topological effects disappear at some critical molecular length and concentration

16 Matrix concentration Chapman, C.E et al, Soft Matter (2012) Entangled Blends of Linear & Ring DNA Fraction of linear DNA in matrix Rapid slowing of circles as linear molecules begin to entangle it

17 Chapman, C.E et al, Soft Matter (2012) Entangled Blends of Linear & Ring DNA For diffusing linear molecules: Non-monotonic dependence of diffusion of linear DNA on fraction of surrounding linear molecules in blend

18 Simulation vs. Experiment Chapman, C.E et al, Soft Matter (2012) Lattice bond-fluctuation model simulations match experimental data in both entangled and unentangled regimes For diffusing linear molecules: Non-monotonic dependence of diffusion of linear DNA on fraction of surrounding linear molecules in blend

19 Simulation vs. Experiment Chapman, C.E et al, Soft Matter (2012) Lattice bond-fluctuation model simulations match experimental data in both entangled and unentangled regimes Non-monotonicity: 2 nd order effect of entangling rings being slowed by increased threading events

20 Program Goals: Goal 2 Develop novel approach and instrumentation that combines optical tweezers and fluorescence microscopy to measure forces resisting displacement of single entangled DNA molecules while simultaneously imaging conformations and dynamics of individual surrounding molecules to allow for direct probing of molecular interactions, stress and strain occurring in real-time at the single-molecule level. Progress towards Achieving Goal 2 Dual function fluorescence force-measuring dual-trap optical tweezers HAS BEEN BUILT Biochemical assays currently being developed for proposed method NEW: Additional microrheology measurement techniques are being developed NEW: Linear oscillatory microrheology measurements carried out for entangled linear DNA

21 Scientific Transitions Progress towards Achieving Goal 2 NEW: Additional microrheology measurement techniques are being developed NEW: Linear oscillatory microrheology measurements carried out for entangled linear DNA

22 Optical Tweezers 1064 nm Tightly focused laser acts as trap for dielectric objects

23 1064 nm Optical Tweezers Measuring forces exerted on trapped spheres y z x Tightly focused laser acts as trap for dielectric objects Objective External Force Condenser z Detector y x F = -k t x

24 Rheology: Measuring Viscoelasticity Bulk Rheology Solid: purely ELASTIC Energy stored STRESS proportional to STRAIN Stress IN PHASE with oscillatory strain Measures large scale response of material to deformation OSCILLATORY STRAIN (g) exerted RESULTANT STRESS (s) on material measured Newtonian fluid: purely VISCOUS Energy dissipation STRESS proportional to strain RATE 90 0 PHASE SHIFT between g and s Polymeric Fluid: Viscoelastic Storage and Dissipation PHASE SHIFT between 0 and 90 0

25 Rheology: Measuring Viscoelasticity Bulk Rheology Dynamic Moduli quantify amount of elasticity and viscosity Elastic/Storage Modulus G = s 0 cos( f) g 0 Measures large scale response of material to deformation OSCILLATORY STRAIN (g) exerted RESULTANT STRESS (s) on material measured Viscous/Loss Modulus G = s 0 sin( f) g 0 Polymeric Fluid: Viscoelastic Storage and Dissipation PHASE SHIFT between 0 and 90 0

26 Rheology: Measuring Viscoelasticity Bulk Rheology Dynamic Moduli quantify amount of elasticity and viscosity Elastic/Storage Modulus G = s 0 cos( f) g 0 Measures large scale response of material to deformation OSCILLATORY STRAIN (g) exerted RESULTANT STRESS (s) on material measured Viscous/Loss Modulus ( ) = ( G w) 2 + ( G w) 2 h w G = s 0 sin( f) g 0 Complex Viscosity é ë 1/2 ù û

27 Microrheology: Measuring Viscoelasticity Microrheology Dynamic Moduli quantify amount of elasticity and viscosity Elastic/Storage Modulus G = s 0 cos( f) g 0 Measures molecular level response of material to deformation OSCILLATORY STRAIN (g) exerted RESULTANT STRESS (s) on material measured Viscous/Loss Modulus ( ) = ( G w) 2 + ( G w) 2 h w G = s 0 sin( f) g 0 Complex Viscosity é ë 1/2 ù û

28 Microrheology: Measuring Viscoelasticity Microrheology Dynamic Moduli quantify amount of elasticity and viscosity g o = 10 mm s o = 1.2 pn f = 90 o Elastic/Storage Modulus Viscous/Loss Modulus G = s 0 cos( f) g 0 G = s 0 sin( f) g 0 g o = 2.5 mm s o = 2.2 pn f = 56 o Water 1 mg/ml 45 kbp linear DNA

29 Microrheology: Measuring Viscoelasticity Microrheology g o = 10 mm s o = 1.2 pn f = 90 o g o = 2.5 mm s o = 2.2 pn f = 56 o Water 1 mg/ml 45 kbp linear DNA

30 Microrheology: Probing the Molecular Level g o = 10 mm s o = 1.2 pn f = 90 o g o = 2.5 mm s o = 2.2 pn f = 56 o Water 1 mg/ml 45 kbp linear DNA

31 Loss Modulus G G ( ), G ( ) [Pa] Storage Modulus G Linear Microrheology Strain Independence for small oscillations: Linear Regime Linear Regime Strain 1 mg/ml 45 kbp linear DNA Strain 45 kbp, 1 mg/ml 115 kbp, 1 mg/ml 45 kbp, 2 mg/ml 11 kbp, 1 mg/ml 45 kbp, 1 mg/ml 115 kbp, 2 mg/ml Oscillation Angular Frequency (rad/s) Length Dependence crossover from primarily viscous to elastic regime

32 G ( ), G ( ) [Pa] Macro- vs. Micro- rheology Strain Independence for small oscillations: Linear Regime 45 kbp, 1 mg/ml 115 kbp, 1 mg/ml 45 kbp, 2 mg/ml 11 kbp, 1 mg/ml 45 kbp, 1 mg/ml 115 kbp, 2 mg/ml Oscillation Angular Frequency (rad/s) Length Dependence crossover from primarily viscous to elastic regime

33 Complex Viscosity [Pa*s] Complex Viscosity DNA Length Dependence 11 kbp, 1 mg/ml 45 kbp, 1 mg/ml 115 kbp, 2 mg/ml Methyl Cellulose Concentration Dependence (Brau 2007) Oscillation Angular Frequency [rad/s] ( ) = ( G w) 2 + ( G w) 2 h w é ë 1/2 ù û

34 Interactions with other Groups COLLABORATIONS: Dr. Douglas E. Smith, University of California, San Diego -USCD Graduate Student carrying out research funded by grant Dr. Sachin Shanbhag, Florida State University -modeling and simulations of diffusion experiments TRAINING OTHER GROUPS: Dr. Julia Kornfield, California Institute of Technology Dr. Gregory McKenna, Texas Tech University -trained groups with polymer rheology expertise in large-scale purification and handling of DNA molecules STUDENT RESEARCHERS: Cole D. Chapman, Graduate Student, University of California, San Diego Kent Lee, Undergraduate, University of San Diego Dean Henze, Undergraduate, University of San Diego

35 Publications Chapman, C. E.; Shanbhag S.; Smith, D. E.; Robertson-Anderson, R. M. Complex effects of molecular topology on diffusion in entangled biopolymer blends Soft Matter, 8, 35, (2012). Invited Talks Anderson, R.M.R. Untangling the physics of entangled DNA Frontiers in Science Seminar Series. Cal State San Marcos (2012). *article on talk in North County Times Funding: Dr. Hugh DeLong AFOSR YIP Acknowledgements Students: Cole E. Chapman Kent Lee Dean Henze Collaborators Doug Smith (UCSD) Sachin Shanbhag (FSU)