We use optical tweezers and fluorescence microscopy techniques to directly determine the remarkable molecular and microscale dynamics that give rise to the rich viscoelastic material properties of a range of biopolymer systems.
Soft squishy materials are complex macromolecular systems that display intriguing and perplexing non-Newtonian viscoelastic properties, especially when the macromolecules (i.e. polymers) are entangled, crowded or cross-linked. Soft matter is all around us - glue, paint, gum, petroleum, athletic and military equipment, and of course – BIOLOGY! Soft materials can behave both as liquids (viscous) AND solids (elastic) depending on the lengths, topologies, flexibility, and concentration of the polymers comprising them. Soft materials can also change their properties in reaction to varying types and degrees of stresses (ever played with silly putty or Ooblek?). The fascinating physics of soft materials can be used to develop new multifunctional, dynamic materials that can be specifically tuned for a wide range of needs.
Because biology naturally produces a wide range of polymers (DNA, RNA and proteins) and soft materials (cells, tissue, tendons, blood, mucus….), biopolymers are the perfect candidates to study to elucidate the captivating mechanics we find in the squishy materials in and all around us.
These important biomolecules vary widely in length, flexibility, and structure. For example, DNA lengths span 6 orders of magnitude from submicron to meter scales and exist in linear, ring and supercoiled forms. Long DNA chains (10-1000 um) are also quite flexible with persistence lengths of 50 nm, orders of magnitude smaller than the molecules themselves. In contrast, the cytoskeleton protein actin forms filaments ~1-20 um long that are only semiflexible with a persistence length of ~17 um.
Click here to read more about our past research using optical tweezers.Crowding DNA Actin Network Dynamics Nonlinear and non-continuum viscoelasticity of entangled DNA Ring DNA Dynamics
Biological cells are extremely crowded environments with typical macromolecular concentrations of ~20 – 40%. Crowding plays a principle role in a wide array of biological processes, such as gene expression, protein folding, binding and aggregation, chromosomal compaction, cell volume regulation, and catalytic enzyme activity. Drug delivery systems, gene therapy, and production and manipulation of synthetic cells and nanomaterials are also highly impacted by cellular crowding. Macromolecular mobility is greatly reduced in crowded environments, yet diffusion remains the primary mechanism by which the majority of reactions and interactions occur. Crowding also alters the conformations and stability of nucleic acids and proteins, greatly impacting protein-DNA binding efficiency, transcription and replication .
- How is DNA mobility altered by varying degrees of crowding?
- Does DNA exhibit anomalous diffusion as seen in other crowded environments?
- Are DNA crowding interactions entropically or enthalpically driven?
- What DNA conformations are most stable when crowded?
- How does the length and topology of the DNA and crowder impact crowding effects?
We are using in vitro fluorescence microscopy, particle tracking and novel image analysis techniques to characterize the effects of crowding on the mobility and conformation of large DNA molecules.
Want to know more? See our: 2015 Soft Matter paper:Universal scaling of crowding-induced DNA mobility is coupled with topology-dependent molecular compaction and elongation 2015 APS March Meeting: Gorczyca Poster
Filamentous actin (F-actin), a semiflexible biopolymer ubiquitous in biological cells, is a key structural protein comprising the cellular cytoskeleton. F-actin plays a critical role in almost all mechanically-driven cellular processes like division, shape change, motility, apoptosis, muscle function, and many others. The versatile biological role of F-actin lies in its unique semiflexible nature, and its ability to form entangled and cross-linked networks that exhibit complex and often nonlinear mechanical responses to strain. Beyond the obvious biological relevance, the semiflexibility of F-actin leads to experimentally accessible (i.e. slow) relaxation dynamics that can reveal molecular-level entangled polymer dynamics.
- What are the molecular-level dynamics and interactions that give rise to the nonlinear mechanical response of entangled actin networks and cells?
- What are the critical length and time scales of the network that control the onset of nonlinear mechanics?
- How do microscale forces induced in an actin network propagate out to meso- and macroscales?
- How do molecular strains and deformations in stressed networks give rise to the apparent resistive stresses and stress relaxation?
- How does the degree of entanglements alter the mechanical response?
- How and why does cross-linking lead to enhanced nonlinearity at the molecular-level?
- What are the molecular-level relaxation mechanisms in cross-linked networks?
We are using optical tweezers microrheology and novel fluorescence labeling techniques to answer the questions above by imposing microscale strains on actin networks while measuring induced forces and tracking individual filaments in the networks.Want to learn more? See our: 2015 APS March Meeting: Blair poster 2015 Soft Matter paper Entangled F-actin displays a unique crossover to microscale nonlinearity dominated by entanglement segment dynamics
Networks of entangled DNA have a number of important lengthscales that can contribute to molecular-level and bulk dynamics including network mesh size, molecular length between entanglements, reptation tube radius, persistence length, radius of gyration, and molecular length. These lengths range from ~50 nm up to 100 um and each lead to different relaxation dynamics and molecular stress and strain responses. Such complexities have led to conflicting and unexplained bulk mechanical response measurements and varying theories to explain discrepancies. While near-equilibrium (linear) rheology measurements can be explained by the reptation model, this agreement breaks down for nonlinear strains that drive the entangled DNA far from equilibrium. This agreement can also breakdown at sufficiently small lengthscales where the network can no longer be treated as a continuum material.
- What are the molecular-level dynamics and interactions that collectively lead to bulk nonlinear stresses induced in entangled flexible polymer materials?
- What are the resistive stresses and relaxation dynamics induced in individual entangled DNA molecules subject to nonlinear strains?
- Why do large strains lead to a breakdown of the reptation model? What molecular mechanisms cause this breakdown?
- What are the dominant molecular length scales and interactions that lead to elasticity in the network?
- At what lengthscales do molecular-level induced stresses no longer map to bulk stresses?
- At what point does the noncontinuum nature of entangled DNA materials matter?
To answer these important questions, we are developing and using optical tweezers microrheology techniques to probe entangled networks of DNA.Want to learn more? See our: 2014 Macromolecules paper Onset of Non-Continuum Effects in Microrheology of Entangled Polymer Solutions
We typically think of biopolymers as long linear chains, but a large class of DNA molecules are circles or rings (with supercoiling relaxed). Beyond the biological importance of ring DNA, blends of ring and linear polymers are favored in practical materials engineering to effectively tune properties such as miscibility and strain hardening. In these blends, rings can become threaded by their linear counterparts, in which case the only way they can move is by the threading linear polymers releasing their constraints (i.e diffusively unthreading themselves). This constraint release process of diffusion is much slower than reptation, and leads to highly complex and varying material properties. Despite the biological and industrial importance of ring DNA, we still don’t really understand how they behave.
- How does closing the ends of a biopolymer affect its dynamics?
- Can ring DNA still entangle with each other? Do ring polymers still reptate?
- How does crowding impact ring DNA?
We are using fluorescence microscopy, particle tracking, image analysis and microfluidics to answer these questions.Want to know more? See our: 2015 collaborative Macromolecules paper:When Ends Meet: Circular DNA Stretches Differently in Elongational Flows 2012 Soft Matter paper:Complex Effects of Molecular Topology on Diffusion in Entangled Biopolymer Blends 2007 PNAS paper:Strong effects of molecular topology on diffusion of entangled DNA molecules 2007 Macromolecules:Direct measurement of the confining forces imposed on a single molecule in a concentrated solution of circular polymers
Traditional experiments probing polymer networks and soft materials are carried out on large numbers of polymers, so molecular-level dynamics can only be inferred from bulk material properties by using theoretical predictions that relate the two. However, over the past few decades microrheology and fluorescence imaging techniques have been developed to enable us to elucidate the molecular-level dynamics that give rise to the perplexing, fascinating and useful properties of soft materials.
Traditional rheology experiments probe the mechanical response of soft materials by applying macroscopic strains to the material and measuring bulk resistive stresses. Microrheology, on the other hand accesses and directly characterizes microscale dynamics by using microspheres that are either passively diffusing or actively driven through the material or network. We specialize in “active” microrheology techniques that use optical tweezers to strain biopolymer networks over a wide dynamical range and measure the molecular-level stresses induced in response to the strains. With these techniques we can characterize both linear and nonlinear molecular response, as well as the transition from one to the other. We can also characterize inhomogeneities and microscale structures present in the network. The images show a few of our measurement schemes.
Linear Oscillatory Microrheology
We oscillate a trapped micro-bead (embedded in a biopolymer solution) at submicron amplitudes, over a range of oscillation frequencies, and measure the force the DNA exerts on the bead during oscillation.
By determining the force amplitude and the phase difference between the force (red curve) and bead displacement (black curve) oscillations we can determine frequency-dependent viscoelastic properties typically measured in traditional macrorheology experiments. For example, we can quantify the elastic (storage) modulus – which quantifies how much elasticity or energy storage the material exhibits; and the viscous (loss) modulus – which quantifies how much fluidity or energy dissipation the material exhibits. Want to know more? See our:
Nonlinear Viscoelastic Recoil
A trapped bead is moved a far distance at fast speeds (relative to the length and time scales of the biopolymer material) to perturb the network far from equilibrium.
In the figure, the bead is blue, the trap center is red and the entangled polymers are green. We measure (i) the force the network exerts (black curve) to resist this extreme perturbation and (ii) how much memory it retains following the strain by tracking how much the bead “bounces back” or “recoils” when we release it from the trap (red curve). Four stages of a sample experiment are shown: (Equilibration) Bead is trapped, bead and DNA solution are allowed to equilibrate; (Strain) Trapped bead is pulled 30 μm at constant speed vtrap through solution (blue curve); (Wait Time) Following strain, trapped bead begins to return to trap center; (Recoil) Trap is shut off and probe recoils backward (red curve) with speed vrecoil. Black curve during Recoil shows full return of bead to trap center (force returns to zero) if the laser is not shut off. Want to know more? See our: 2015 Soft Matter paper “Entangled F-actin displays a unique crossover to microscale nonlinearity dominated by entanglement segment dynamics
Fluorescence Microscopy & Single-Molecule Tracking
We can actually see single DNA and actin molecules wiggling around using fluorescence microscopy. We do so by attaching fluorescent dye molecules uniformly along the biopolymer that emit light of a specific wavelength when they are “excited” by light of another specific wavelength.
By using filters to only allow the excitation light wavelength to hit the sample and the wavelength emitted by the dye molecules to reach the camera, we can selectively image single labeled DNA and actin molecules within biopolymer networks.
As shown, for flexible DNA molecules diffusing in entangled or crowded networks, we can track the center-of-intensity (analogous to center-of-mass) and the lengths of the major and minor axes of the DNA “blob” over time. From these quantities we can characterize both molecular mobility as well as conformational dynamics.
Want to know more? See our: 2015 Soft Matter paper: Universal scaling of crowding-induced DNA mobility is coupled with topology-dependent molecular compaction and elongation. 2015 APS March Meeting: Gorczyca Poster. 2012 Soft Matter paper: Complex Effects of Molecular Topology on Diffusion in Entangled Biopolymer Blends.
For semiflexible F-actin, uniform labeling allows us to measure molecular lengths, persistence lengths, and network mesh size.
As shown, we use confocal microscopy and filament-surface attachment to measure the distribution of actin filament lengths in entangled actin networks. Want to know more? See our: 2015 Soft Matter paper: Entangled F-actin displays a unique crossover to microscale nonlinearity dominated by entanglement segment dynamics.
Discrete filament labeling
We can also use specialized shearing/annealing techniques to discretely label small uniformly spaced segments along actin filaments. Discrete labeling allows us to track individual points along a filament to characterize segmental dynamics and filament deformation under strain.Want to know more? See our: 2015 APS March Meeting: Falzone Talk. Read the next section!
Combined Force-Fluorescence Measurements
Both optical tweezers and fluorescence microscopy, when used independently can shed a wealth of new light on the molecular dynamics and interactions of entangled biopolymers, but they can’t directly connect microscale forces to the corresponding molecular deformations and dynamics.
- What are the biopolymers in the network doing to produce the force they exert on a microsphere moving through the network?
- How do biopolymers deform and relax during and following imposed forces?
As shown below, one of our most recent technological advancements combines both single-molecule methods to simultaneously and directly measure microscale forces exerted at the strain site while tracking the motion of the molecular segments exerting these forces.
(a) Depiction of tracking labeled segments along an actin filament. (b) Microscope image of actin filament with interspersed ~0.45-μm labeled segments. The centroid of each spot is tracked over the time course of the experiment. (c) Tracking segments at varying distances from the strain path. 4.5-μm bead (orange circles) is pulled through the discretely-labeled actin network. Dotted lines outline annuli positioned every 9 μm from strain path (4.5, 13.5…49.5 μm). We track labeled segments within each annulus to determine dependence of segment deformation on distance from strain. All segment tracks 22.5 μm from the strain are shown. (d) We measure tracked segment displacements and force induced on trapped bead over 3 phases: Equilibrium [no trap movement]; Strain [trapped bead pulled through network at constant speed; Recovery [no trap movement, deformed entanglements recover]. Average x-displacement of tracked filaments (blue triangles), force exerted on bead (green circles), and trap position (red line, axis not shown) are shown.Want to know more? See our: 2015 APS March Meeting: Blair Poster.
In a Nutshell: Reptation Model for Entangled Polymers
When the molecules comprising polymer systems are entangled with each other, the 1979 Nobel-prize winning Reptation Tube Model, pioneered by P.G. De Gennes and advanced by Doi and Edwards, predicts that each molecule is confined to a tube-like region formed by the surrounding constraints. So each molecule can only slither like a snake in a direction parallel to its contour – a diffusive process termed reptation. When the molecules are stressed or strained the tubes deform but maintain their size.
In other words, the spacing between entanglements doesn’t change. The polymers relax this stress by diffusing out of deformed tubes into new unperturbed tubes. The reptation tube model has been wildly successful in accurately modeling entangled polymer dynamics in most regimes. However, the beauty and elegance of this model lies in its simplicity, which inevitably can’t account for every regime and variant of biopolymer fluids and soft matter. Want to know more? See our: M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Science Publications Vol. 73 (Oxford University Press, New York, 1986). Some open questions about this model that our research aims to answer are:
- Is the reptation model always valid??
- What happens when the polymers are circles with no ends??
- What if the surrounding molecules have different sizes or topologies?
- Can the tubes change size and shape or even be destroyed under strain?
In a Nutshell: Force-measuring optical tweezers:
An infrared laser that is tightly focused by a microscope objective acts as a trap for dielectric objects like microspheres. The trap acts much like a spring, so when a trapped micro-bead is pulled from the trap a restoring force acts to bring the bead back to the trap center.
The trap is formed because the combined momentum of the laser light and the dielectric bead must be conserved. As the laser passes through a bead that has been pushed from the trap center, the light is bent, changing its momentum, which in turn imparts a force on the bead returning it to the center of the trap.The more the trapped bead is pulled from the trap center (by say entangled biopolymers pulling on it), the more the exiting laser beam is deflected. In fact the exiting beam deflection is simply proportional to the external force exerted on the trapped bead (Hooke’s law!). So we can determine the force exerted on the trapped bead by measuring the beam deflection with a photodiode position-sensing detector.
By splitting the laser beam into two separate polarizations we can also form two traps – one from each polarization.
We can embed micro-beads in biopolymer networks and other soft materials to induce microscale strains on the materials (by pulling a trapped bead through the network), and measure the force the molecules exert on the trapped bead to oppose the strain. This is the basis of active microrheology.