Optical Tweezers Experiments Research Articles

Theory of optical-tweezers forces near a plane interface

Optical-tweezers experiments in molecular and cell biology often take place near the surface of the microscope slide that defines the bottom of the sample chamber. There, as elsewhere, force measurements require force-calibrated tweezers. In bulk, one can calculate the tweezers force from first principles, as recently demonstrated. Near the surface of the microscope slide, this absolute calibration method fails because it does not account for reverberations from the slide of the laser beam scattered by the trapped microsphere. Nor does it account for evanescent waves arising from total internal reflection of wide-angle components of the strongly focused beam. In the present work we account for both of these phenomena. We employ Weyl's angular spectrum representation of spherical waves in terms of real and complex rays and derive a fast-converging recursive series of multiple reflections that describes the reverberations, including also evanescent waves. Numerical simulations for typical setup parameters evaluate these effects on the optical force and trap stiffness, with emphasis on axial trapping. Results are in good agreement with available experimental data. Thus, absolute calibration now applies to all situations encountered in practice.

Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers.

Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain—And consequently its persistence length—Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot–knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems—Be they artificial or biologica in origin—And for their technological application.

Active microrheology of colloidal suspensions: Simulation and microstructural theory

Discrete particle simulations by accelerated Stokesian dynamics (ASD) and a microstructural theory are applied to study the structure and viscosity of hard-sphere Brownian suspensions in active microrheology (MR). The work considers moderate to dense suspensions, from near to far from equilibrium conditions. The microscopic theory explicitly considers many-body hydrodynamic interactions in active MR and is compared with the results of ASD simulations, which include detailed near- and far-field hydrodynamic interactions. We consider probe and bath particles which are spherical and of the same radius a. Two conditions of moving the probe sphere are considered: These apply constant force (CF) and constant velocity (CV), which approximately model magnetic bead and optical tweezer experiments, respectively. The structure is quantified using the probability distribution of colloidal particles around the probe, Pb|p(r)=ng(r), giving the probability of finding a bath particle centered at a vector position r relative to a moving probe particle instantaneously centered at the origin; n is the bath particles number density, and is related to the suspension solid volume fraction, ϕ, by n=3ϕ/4πa3. The pair distribution function for the bath particles relative to the probe, g(r), is computed as a solution to the pair Smoluchowski equation (SE) for 0.2≤ϕ≤0.50, and a range of Péclet numbers, describing the ratio of external force on the probe to thermal forces and defined as Pef=Fexta/(kbT) and PeU=6πηUexta2/(kbT) for CF and CV conditions, respectively. Results of simulation and theory demonstrate that a wake zone depleted of bath particles behind the moving probe forms at large Péclet numbers, while a boundary-layer accumulation develops upstream and near the probe. The wake length saturates at Pef≫1 for CF, while it continuously grows with PeU in CV. This contrast in behavior is related to the dispersion in the motion of the probe under CF conditions, while CV motion has no dispersion; the dispersion is a direct result of many-body nonthermal interactions. This effect is incorporated in the theory as a force-induced diffusion flux in pair SE. We also demonstrate that, despite this difference of structure in the two methods of moving the probe, the probability distribution of particles near the probe is primarily set by the Péclet number, for both CF and CV conditions, in agreement with dilute theories; as a consequence, similar values for apparent viscosity are found for the CF and CV conditions. Using the microscopic theory, the structural anisotropy and Brownian viscosity near equilibrium are shown to be quantitatively similar in both CF and CV motions, which is in contrast with the dilute theory which predicts larger distortions and Brownian viscosities in CV, by a factor of two relative to CF MR. This difference relative to dilute theory arises due to the determining role of many-body interactions associated with the underlying equilibrium structure in the semidilute to concentrated regime.

Knotting and unknotting of a protein in single molecule experiments

Spontaneous folding of a polypeptide chain into a knotted structure remains one of the most puzzling and fascinating features of protein folding. The folding of knotted proteins is on the timescale of minutes and thus hard to reproduce with atomistic simulations that have been able to reproduce features of ultrafast folding in great detail. Furthermore, it is generally not possible to control the topology of the unfolded state. Single-molecule force spectroscopy is an ideal tool for overcoming this problem: by variation of pulling directions, we controlled the knotting topology of the unfolded state of the 52-knotted protein ubiquitin C-terminal hydrolase isoenzyme L1 (UCH-L1) and have therefore been able to quantify the influence of knotting on its folding rate. Here, we provide direct evidence that a threading event associated with formation of either a 31 or 52 knot, or a step closely associated with it, significantly slows down the folding of UCH-L1. The results of the optical tweezers experiments highlight the complex nature of the folding pathway, many additional intermediate structures being detected that cannot be resolved by intrinsic fluorescence. Mechanical stretching of knotted proteins is also of importance for understanding the possible implications of knots in proteins for cellular degradation. Compared with a simple 31 knot, we measure a significantly larger size for the 52 knot in the unfolded state that can be further tightened with higher forces. Our results highlight the potential difficulties in degrading a 52 knot compared with a 31 knot.

Chirality modifies the interaction between knots

In this study we consider an idealization of a typical optical tweezers experiment involving a semiflexible double-knotted polymer, with steric hindrance and persistence length matching those of dsDNA in high salt concentration, under strong stretching. Using exhaustive molecular-dynamics simulations we show that not only does a double-knotted dsDNA filament under tension possess a free-energy minimum when the two knots are intertwined, but also that the depth of this minimum depends on the relative chirality of the two knots. We rationalize this dependence of the effective interaction on the chirality in terms of a competition between chain entropy and bending energy.

Mechanisms of backtrack recovery by RNA polymerases I and II

During DNA transcription, RNA polymerases often adopt inactive backtracked states. Recovery from backtracks can occur by 1D diffusion or cleavage of backtracked RNA, but how polymerases make this choice is unknown. Here, we use single-molecule optical tweezers experiments and stochastic theory to show that the choice of a backtrack recovery mechanism is determined by a kinetic competition between 1D diffusion and RNA cleavage. Notably, RNA polymerase I (Pol I) and Pol II recover from shallow backtracks by 1D diffusion, use RNA cleavage to recover from intermediary depths, and are unable to recover from extensive backtracks. Furthermore, Pol I and Pol II use distinct mechanisms to avoid nonrecoverable backtracking. Pol I is protected by its subunit A12.2, which decreases the rate of 1D diffusion and enables transcript cleavage up to 20 nt. In contrast, Pol II is fully protected through association with the cleavage stimulatory factor TFIIS, which enables rapid recovery from any depth by RNA cleavage. Taken together, we identify distinct backtrack recovery strategies of Pol I and Pol II, shedding light on the evolution of cellular functions of these key enzymes.

TFAM Regulates Mitochondrial Transcription through Sequence-Specific DNA Looping

Mitochondrial transcription factor A (TFAM) is an abundant human mitochondrial High Mobility Group Box (HMGB) protein. TFAM is an architectural protein that shapes mitochondrial DNA (mtDNA) and regulates mitochondrial transcription. Sequence-specific binding of TFAM to DNA upstream of the light-strand promoter (LSP) leads to bending that correlates with transactivation of this promoter. Here we use a dual promoter construct containing both LSP, HSP1 and the natural inter-promoter region (IPR) to understand how TFAM binding governs transcription activation. We show that the IPR contributes to TFAM transactivation of HSP1, while removal of the carboxyl-terminal tail of TFAM (TFAM-ΔCT26) leads to a complete loss of transactivation of HSP1, with only minimal effects on LSP, suggesting a different biophysical mechanism for TFAM-mediated transcription activation from HSP1. To understand the mechanism by which TFAM activates HSP1 transcription, we used atomic force microscopy (AFM) in liquid to probe the effect of TFAM on the IPR construct. We observe that at the low concentrations of TFAM where transcription activation is high, TFAM induces the formation of DNA loops in a region defined by the IPR, with TFAM present at the strand crossing point. Under the same conditions, TFAM-ΔCT26 fails to induce DNA looping. While random DNA also forms loops in the presence of TFAM, TFAM is twice as likely to mediate the loops when the IPR sequence is present. Optical tweezers experiments also demonstrate that TFAM stabilizes DNA loops, which require significant force to break. Taken together, our results are consistent with sequence-specific DNA looping contributing to TFAM transactivation of HSP1, suggesting that unique mechanisms are employed for TFAM-dependent transcription at LSP and HSP1.

Single Molecule Fluorescence Studies of Transition Paths in DNA Hairpin Folding

DNA hairpins are the simplest structures for investigating fundamental aspects of nucleic acid folding mechanisms. For hairpins exhibiting two-state behavior, all of the mechanistic information on how the hairpin folds is contained in the transition path, the rare event in single molecule trajectories when the free energy barrier between folded and unfolded states is actually crossed. In the only experimental study of transition paths in nucleic acids to date, Woodside and coworkers measured an upper bound of 50 μs for the average transition path times (TPT) of several nucleic acids, limited by the time resolution of their optical tweezer experiments (Neupane et al. Phys. Rev. Lett. 2012). Neupane et al. also reconstructed the free energy surface for an indirect determination of average transition path times from Szabo's analytical theory for diffusive barrier crossing. We used confocal single molecule FRET to study a DNA hairpin with 4 base pairs in the stem and 21 T's in the loop and that has a folding time of 310 μs in 500mM NaCl at 22oC. Maximum likelihood analysis of 780 transitions in photon trajectories yielded an upper bound of 2.5 μs for the average transition path time (Truex et al., Phys. Rev. Lett. 2015), compared to the value of ∼4 μs predicted by Neupane et al. from hairpins with 9-30 base pair stems and 4 T's in the loop, providing an important test of energy landscape theory. Current experiments are aimed at reducing blinking, a major obstacle to measuring transition path times, and at eventually characterizing structural changes during transition paths, which will provide a very demanding test of mechanisms predicted by both theoretical models and simulations.

Significance of Steric Bulk in DNA Threading Intercalation Revelaed through Force-Dependent Kinetics

DNA threading intercalation is a DNA binding mode, whereby a molecule must thread a bulky group through the DNA duplex to allow a planar central section to stack with the DNA base pairs. Molecules that bind to DNA via threading intercalation display incredibly slow association and dissociation kinetics. This is a result of the large duplex deformations required for the ligand to thread and unthread the DNA. While this binding mode has been investigated extensively, the specific molecular characteristics that affect the binding to DNA are still poorly understood. This study utilizes single molecule stretching with optical tweezers to elucidate the effects that the bulk and geometry of the threading moieties have on DNA binding. Single molecule optical tweezers experiments are a powerful tool in analyzing threading intercalation because they allow for direct quantification of both the equilibrium behavior and kinetics of DNA-ligand binding. The equilibrium binding profile of the binuclear ruthenium complex ΔΔ-[μ-bidppz(bipy)4Ru2]4+ (ΔΔ-B) was quantified in this study, revealing a dissociation constant on the same order of magnitude as its previously studied, bulkier sister molecule ΔΔ-[μ-bidppz(phen)4Ru2]4+ (ΔΔ-P). ΔΔ-B shows faster on rates compared to ΔΔ-P at low force, while both on rates converge to comparable values at high force. The off rates of ΔΔ-B show no force dependence, whereas the off rates of ΔΔ-P are strongly facilitated by force. These results suggest that in the absence of force that ΔΔ-B threads DNA faster and unthreads slower, making ΔΔ-B a more ideal DNA binding anticancer drug.

Force Spectroscopy of Nucleosomes at the Promoters of the Lh Genes Reveals two Distinct Strategies for their Regulation

Luteinizing hormone (LH) is a heterodimeric protein that regulates function of the gonads, and is composed of two subunits, which are encoded by two different genes: chorionic gonadotropin-a (Cga) and Lhs. A sequence-based algorithm designed to predict nucleosome positions on DNA suggests that the promoters of both genes, and in particular the binding regions for important transcription factors, are packed into nucleosomes. Since gene expression requires that the promoter be accessible to the cellular transcription machinery, we hypothesized that nucleosome positioning regulates basal expression of these genes. We are performing single-molecule force spectroscopy with optical tweezers, complemented by MNase mapping, to probe the architecture of chromatin on both gene promoters. In gonadotrope cells, the promoter of Lhs is occupied by a nucleosome containing the variant H2A.Z, while the Cga promoter appears nucleosome-depleted. Optical tweezers experiments show that a nucleosome reconstituted on the Cga promoter is weaker, and poorly localized, as compared to the one on the promoter of LHs. This may suggest that it is evicted, in vivo, by chromatin remodelers. In contrast, the first nucleosome downstream of the transcription start site contains H2A.Z in Cga but H2A in Lhs, and is well localized on both genes, although more weakly bound on the Lhs than the Cga gene. Hence, these two genes are apparently regulated by distinct strategies, tailored to obtain higher expression for Cga, which encodes a subunit shared also by other hormones, and lower for Lhs, which is unique to this hormone. Our results highlight how DNA sequence, the usage of alternative histone variants and, possibly, remodeling machinery act synergistically to modulate gene expression.

Mechanical Unfolding of E. Coli RNase H Reveals an Intermediate with a Force-Induced Shift in the Rate-Limiting Barrier

Previous observations of the mechanical unfolding of E. coli RNase H∗ (ecRNH∗) indicated a single, cooperative transition from the native, folded state to the unfolded polypeptide. However, higher resolution single molecule optical tweezers experiments now demonstrate an obligate unfolding intermediate. Moreover, we find that with increasing force the transition from the native state to the unfolding intermediate becomes the rate-limiting barrier to complete unfolding of the protein. That is, under low force, the unfolding of the protein is kinetically limited by the transition from the intermediate to the completely unfolded state. We sought to determine the region of the protein that unfolds in the intermediate. Unfolding of the C-terminal E-helix is consistent with the measured extension change (∼33 amino acids), and the optical tweezers pulling geometry from the N- and C-termini. We utilize mutational analysis in the E-helix and other locations within ecRNH∗ to probe the unfolding kinetics. We dovetail our single molecule experiments with bulk, zero-force denaturant unfolding to quantify the effects on the energy landscape by the amino acid substitutions. The bulk kinetic and thermodynamic parameters are also used to understand the rate-limiting barrier to unfolding by these complementary methods. Our results show that destabilizing mutations in the core of the protein have no effect on the unfolding kinetics. In contrast, destabilizing mutations in the E-helix and periphery of the protein increase the rate of unfolding both in bulk and single molecule experiments. These results further corroborate that the E-helix is unfolded in the unfolded intermediate state of the protein.

Mechanical Force and Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot

Mechanical resistance of pseudoknot (PK) in mRNA deemed relevant in stimulating programmed ribosomal frameshifting (PRF) has lead to a number of single molecule pulling experiments in order to decipher the PRF mechanism. Motivated by these studies, we performed simulations to describe the response of a Beet Western Yellow Virus (BWYV) PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs) using a coarse-grained model. The simulations based on the model quantitatively reproduces the three-stage thermal melting of BWYV PK and the stability of the folded state (F) with respect to the unfolded state (U) inferred in ensemble experiments setting the stage for making testable predictions. The predicted phase diagram in the [C, f] plane shows that a sequence of structural transitions populating intermediates occur as f and C are changed. The least stable tertiary interactions rupture first followed by unfolding of the 3′-end hairpin. Finally, the most stable 5′-end hairpin unravels producing a stretched state. A theoretical analysis of the phase boundaries, separating the F and an intermediate state (I), and I and U states shows that the critical force for rupture scales as (log Cm)α with α=1 (=0.5) for U−I (I−F) transition. This relation is used to obtain the ion-preferential coefficients, which suggests that ion-RNA interactions can be quantitatively measured using laser optical tweezers experiments. We predict that −1 PRF efficiency should be determined by the stability of the 5′ hairpin that the ribosome first encounters. A good correlation between the increase in −1 PRF efficiency and increase in the stability of 5′ hairpin supports this prediction.

Phi29 Connector-DNA Interactions Govern DNA Crunching and Rotation, Supporting the Check-Valve Model

During replication of the ϕ29 bacteriophage inside a bacterial host cell, a DNA packaging motor transports the viral DNA into the procapsid against a pressure difference of up to 40 ± 20 atm. Several models have been proposed for the underlying molecular mechanism. Here we have used molecular dynamics simulations to examine the role of the connector part of the motor, and specifically the one-way revolution and the push-roll model. We have focused at the structure and intermolecular interactions between the DNA and the connector, for which a near-complete structure is available. The connector is found to induce considerable DNA deformations with respect to its canonical B-form. We further assessed by force-probe simulations to which extent the connector is able to prevent DNA leakage and found that the connector can act as a partial one-way valve by a check-valve mechanism via its mobile loops. Analysis of the geometry, flexibility, and energetics of channel lysine residues suggested that this arrangement of residues is incompatible with the observed DNA packaging step-size of ∼2.5 bp, such that the step-size is probably determined by the other components of the motor. Previously proposed DNA revolution and rolling motions inside the connector channel are both found implausible due to structural entanglement between the DNA and connector loops that have not been resolved in the crystal structure. Rather, in the simulations, the connector facilitates minor DNA rotation during the packaging process compatible with recent optical-tweezers experiments. Combined with the available experimental data, our simulation results suggest that the connector acts as a check-valve that prevents DNA leakage and induces DNA compression and rotation during DNA packaging.

Nucleotides regulate the mechanical hierarchy between subdomains of the nucleotide binding domain of the Hsp70 chaperone DnaK

The regulation of protein function through ligand-induced conformational changes is crucial for many signal transduction processes. The binding of a ligand alters the delicate energy balance within the protein structure, eventually leading to such conformational changes. In this study, we elucidate the energetic and mechanical changes within the subdomains of the nucleotide binding domain (NBD) of the heat shock protein of 70 kDa (Hsp70) chaperone DnaK upon nucleotide binding. In an integrated approach using single molecule optical tweezer experiments, loop insertions, and steered coarse-grained molecular simulations, we find that the C-terminal helix of the NBD is the major determinant of mechanical stability, acting as a glue between the two lobes. After helix unraveling, the relative stability of the two separated lobes is regulated by ATP/ADP binding. We find that the nucleotide stays strongly bound to lobe II, thus reversing the mechanical hierarchy between the two lobes. Our results offer general insights into the nucleotide-induced signal transduction within members of the actin/sugar kinase superfamily.

Titin Domains Progressively Unfolded by Force Are Homogenously Distributed along the Molecule

Titin is a giant filamentous protein of the muscle sarcomere in which stretch induces the unfolding of its globular domains. However, the mechanisms of how domains are progressively selected for unfolding and which domains eventually unfold have for long been elusive. Based on force-clamp optical tweezers experiments we report here that, in a paradoxical violation of mechanically driven activation kinetics, neither the global domain unfolding rate, nor the folded-state lifetime distributions of full-length titin are sensitive to force. This paradox is reconciled by a gradient of mechanical stability so that domains are gradually selected for unfolding as the magnitude of the force field increases. Atomic force microscopic screening of extended titin molecules revealed that the unfolded domains are distributed homogenously along the entire length of titin, and this homogeneity is maintained with increasing overstretch. Although the unfolding of domains with progressively increasing mechanical stability makes titin a variable viscosity damper, the spatially randomized variation of domain stability ensures that the induced structural changes are not localized but are distributed along the molecule's length. Titin may thereby provide complex safety mechanims for protecting the sarcomere against structural disintegration under excessive mechanical conditions.

Optical trapping of the anisotropic crystal nanorod.

We observed in the optical tweezers experiment that some anisotropic nanorod was stably trapped in an orientation tiled to the beam axis. We explain this trapping with the T-matrix calculation. As the vector spherical wave functions do not individually satisfy the anisotropic vector wave equation, we expand the incident and scattered fields in the isotropic buffer in terms of E→, and the internal field in the anisotropic nanoparticle in terms of D→, and use the boundary condition for the normal components of D→ to compute the T-matrix. We found that when the optical axes of an anisotropic nanorod are not aligned to the nanorod axis, the nanorod may be trapped stably at a tilted angle, under which the lateral torque equals to zero and the derivative of the torque is negative.

Red Blood Cell Aging During Storage, Studied Using Optical Tweezers Experiment

This paper presents experimental and numerical studies of erythrocyte stretching, with a focus on the aging of red blood cells in an in vitro environment during storage. The experimental studies were performed using optical tweezers. The laser beam was used to pull and stretch a cell sedimented on a flat surface. A force calibration was obtained via a comparison of the experimental data with results from finite element simulations of the cell stretching. The experiments were performed using blood samples from blood bank donations made by three donors. The experiments were performed over 21 days of storage, and the estimate erythrocyte membrane shear modulus during this period increased from 2.5 to 13 μN/m.

Single-molecule kinetics and footprinting of DNA bis-intercalation: the paradigmatic case of Thiocoraline.

DNA bis-intercalators are widely used in molecular biology with applications ranging from DNA imaging to anticancer pharmacology. Two fundamental aspects of these ligands are the lifetime of the bis-intercalated complexes and their sequence selectivity. Here, we perform single-molecule optical tweezers experiments with the peptide Thiocoraline showing, for the first time, that bis-intercalation is driven by a very slow off-rate that steeply decreases with applied force. This feature reveals the existence of a long-lived (minutes) mono-intercalated intermediate that contributes to the extremely long lifetime of the complex (hours). We further exploit this particularly slow kinetics to determine the thermodynamics of binding and persistence length of bis-intercalated DNA for a given fraction of bound ligand, a measurement inaccessible in previous studies of faster intercalating agents. We also develop a novel single-molecule footprinting technique based on DNA unzipping and determine the preferred binding sites of Thiocoraline with one base-pair resolution. This fast and radiolabelling-free footprinting technique provides direct access to the binding sites of small ligands to nucleic acids without the need of cleavage agents. Overall, our results provide new insights into the binding pathway of bis-intercalators and the reported selectivity might be of relevance for this and other anticancer drugs interfering with DNA replication and transcription in carcinogenic cell lines.

Quantitative DNA Binding, Looping, and Compaction Properties of the HIV-1 Viral Protein R

Human immunodeficiency virus type 1 (HIV-1) Viral protein R (Vpr) is packaged into virions (∼200 molecules) and is essential for viral replication. While several in vivo functions have been attributed to Vpr, one primary function is believed to be transport of the HIV-1 pre-integration complex into the nucleus. Because the nuclear pore diameter is approximately 25 nm, the DNA must be highly compact in order to enter the nucleus. To understand the mechanism by which Vpr may facilitate this nuclear transport, we combine single molecule stretching and atomic force microscopy (AFM). We measure the DNA binding affinity of Vpr for the first time. We then investigate the ability of Vpr to both bind and compact DNA. To do this, we hold DNA at low force for fixed times, allowing it to form loops and other compact structures. We find that the timescale required for the formation of large loops due to protein-DNA bridging is several minutes. In contrast, by holding the DNA molecule at a constant force of 15 pN and measuring its length change, Vpr can also actively compact DNA on the timescale of tens of seconds (15 ± 2 s), representing a different compaction process involving DNA shortening likely due to Vpr binding alone. The persistence length determined from AFM at a low concentration is much longer than that of bare DNA, suggesting that Vpr forms shorter but more rigid structures upon binding DNA. AFM images also demonstrate DNA bridging between strands, consistent with the looping observed in optical tweezers experiments. These results support a model in which Vpr translocates the viral DNA into the nucleus by forming compact structures mediated by protein-DNA and protein-protein interactions.

Brownian Dynamics Study of DNA Supercoil Relaxation

The stresses induced in DNA during cell processes such as replication and transcription lead to the formation of plectonemic supercoils. Supercoiling in turn affects these processes. As a result of this relationship between supercoiling and these processes, the degree of supercoiling in DNA needs to be controlled closely in order to optimize these cell processes. This control is facilitated by enzymes such as type 1b topoisomerases and nicking endonucleases which relax supercoiling in DNA.The dynamics of DNA supercoil relaxation have been studied in recent experiments by means of single-molecule magnetic and/or optical tweezer experiments. Novel as these experiments are, they do not permit a direct observation of the structural changes that occur in DNA during supercoil relaxation. They depend on components (e.g. a paramagnetic bead) attached to the DNA to indirectly obtain information about these dynamics.We studied the dynamics of supercoil relaxation by means of Brownian Dynamics simulations of a discrete wormlike-chain (dWLC) model of DNA. These simulations parallel the single-molecule experiments in which a single DNA molecule is held under constant tension so that its end-to-end extension increases as supercoils are relaxed by a nicking endonuclease. The dWLC model accounts for elasticity, electrostatics and entropic forces as well as for hydrodynamic interactions.From the simulation results, we more directly extract the rate at which supercoiling in DNA is relaxed by nicking endonucleases. We also determine the dependence of the relaxation timescales on the tension applied to the DNA molecule.