Stress-induced structural transitions in DNA and proteins

An Introduction to Magnetic Tweezers

Magnetic tweezers are a single-molecule force and torque spectroscopy technique that enable the mechanical interrogation in vitro of biomolecules, such as nucleic acids and proteins. They use a magnetic field originating from either permanent magnets or electromagnets to attract a magnetic particle, thus stretching the tethering biomolecule. They nicely complement other force spectroscopy techniques such as optical tweezers and atomic force microscopy (AFM) as they operate as a very stable force clamp, enabling long-duration experiments over a very broad range of forces spanning from 10 fN to 1 nN, with 1-10 milliseconds time and sub-nanometer spatial resolution. Their simplicity, robustness, and versatility have made magnetic tweezers a key technique within the field of single-molecule biophysics, being broadly applied to study the mechanical properties of, e.g., nucleic acids, genome processing molecular motors, protein folding, and nucleoprotein filaments. Furthermore, magnetic tweezers allow for high-throughput single-molecule measurements by tracking hundreds of biomolecules simultaneously both in real-time and at high spatiotemporal resolution. Magnetic tweezers naturally combine with surface-based fluorescence spectroscopy techniques, such as total internal reflection fluorescence microscopy, enabling correlative fluorescence and force/torque spectroscopy on biomolecules. This chapter presents an introduction to magnetic tweezers including a description of the hardware, the theory behind force calibration, its spatiotemporal resolution, combining it with other techniques, and a (non-exhaustive) overview of biological applications.

Modeling the Homologous Recombination Process: Methods, Successes and Challenges

Homologous recombination (HR) is a fundamental process common to all species. HR aims to faithfully repair DNA double strand breaks. HR involves the formation of nucleoprotein filaments on DNA single strands (ssDNA) resected from the break. The nucleoprotein filaments search for homologous regions in the genome and promote strand exchange with the ssDNA homologous region in an unbroken copy of the genome. HR has been the object of intensive studies for decades. Because multi-scale dynamics is a fundamental aspect of this process, studying HR is highly challenging, both experimentally and using computational approaches. Nevertheless, knowledge has built up over the years and has recently progressed at an accelerated pace, borne by increasingly focused investigations using new techniques such as single molecule approaches. Linking this knowledge to the atomic structure of the nucleoprotein filament systems and the succession of unstable, transient intermediate steps that takes place during the HR process remains a challenge; modeling retains a very strong role in bridging the gap between structures that are stable enough to be observed and in exploring transition paths between these structures. However, working on ever-changing long filament systems submitted to kinetic processes is full of pitfalls. This review presents the modeling tools that are used in such studies, their possibilities and limitations, and reviews the advances in the knowledge of the HR process that have been obtained through modeling. Notably, we will emphasize how cooperative behavior in the HR nucleoprotein filament enables modeling to produce reliable information.

'Phase transitions' in bacteria - From structural transitions in free living bacteria to phenotypic transitions in bacteria within biofilms

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

DNA fluctuations reveal the size and dynamics of topological domains

DNA supercoiling is a key regulatory mechanism that orchestrates DNA readout, recombination, and genome maintenance. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here, we present a methodology to determine the size and dynamics of topological domains in supercoiled DNA in real time and at the single-molecule level. Our approach is based on quantifying the extension fluctuations-in addition to the mean extension-of supercoiled DNA in magnetic tweezers (MT). Using a combination of high-speed MT experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We find that in the plectonemic regime, the extension variance increases linearly with increasing supercoiling density and show how this enables us to determine the formation and size of topological domains. In addition, we demonstrate how the transient (partial) dissociation of DNA-bridging proteins results in the dynamic sampling of different topological states, which allows us to deduce the torsional stiffness of the plectonemic state and the kinetics of protein-plectoneme interactions. We expect our results to further the understanding and optimization of magnetic tweezer measurements and to enable quantification of the dynamics and reaction pathways of DNA processing enzymes in the context of physiologically relevant forces and supercoiling densities.

On the stability of stalled RNA polymerase and its removal by RapA

Stalling of the transcription elongation complex formed by DNA, RNA polymerase (RNAP) and RNA presents a serious obstacle to concurrent processes due to the extremely high stability of the DNA-bound polymerase. RapA, known to remove RNAP from DNA in an ATP-dependent fashion, was identified over 50 years ago as an abundant binding partner of RNAP; however, its mechanism of action remains unknown. Here, we use single-molecule magnetic trapping assays to characterize RapA activity and begin to specify its mechanism of action. We first show that stalled RNAP resides on DNA for times on the order of 10⁶ seconds and that increasing positive torque on the DNA reduces this lifetime. Using stalled RNAP as a substrate we show that the RapA protein stimulates dissociation of stalled RNAP from positively supercoiled DNA but not negatively supercoiled DNA. We observe that RapA-dependent RNAP dissociation is torque-sensitive, is inhibited by GreB and depends on RNA length. We propose that stalled RNAP is dislodged from DNA by RapA via backtracking in a supercoiling- and torque-dependent manner, suggesting that RapA’s activity on transcribing RNAP in vivo is responsible for resolving conflicts between converging polymerase molecular motors.

Mechanical response to tension and torque of molecular chains via statistically interacting particles associated with extension, contraction, twist, and supercoiling

A methodology for the statistical mechanical analysis of polymeric chains under tension introduced previously is extended to include torque. The response of individual bonds between monomers or of entire groups of monomers to a combination of tension and torque involves, in the framework of this method of analysis, the (thermal or mechanical) activation of a specific mix of statistically interacting particles carrying quanta of extension or contraction and quanta of twist or supercoiling. The methodology, which is elucidated in applications of increasing complexity, is capable of describing the conversion between twist chirality and plectonemic chirality in quasistatic processes. The control variables are force or extension and torque or linkage (a combination of twist and writhe). The versatility of this approach is demonstrated in two applications relevant and promising for double-stranded DNA under controlled tension and torque. One application describes conformational transformations between (native) B-DNA, (underwound) S-DNA, and (overwound) P-DNA in accord with experimental data. The other application describes how the conversion between a twisted chain and a supercoiled chain accommodates variations of linkage and excess length in a buckling transition.

Supercoiling and looping promote DNA base accessibility and coordination among distant sites

DNA in cells is supercoiled and constrained into loops and this supercoiling and looping influence every aspect of DNA activity. We show here that negative supercoiling transmits mechanical stress along the DNA backbone to disrupt base pairing at specific distant sites. Cooperativity among distant sites localizes certain sequences to superhelical apices. Base pair disruption allows sharp bending at superhelical apices, which facilitates DNA writhing to relieve torsional strain. The coupling of these processes may help prevent extensive denaturation associated with genomic instability. Our results provide a model for how DNA can form short loops, which are required for many essential processes, and how cells may use DNA loops to position nicks to facilitate repair. Furthermore, our results reveal a complex interplay between site-specific disruptions to base pairing and the 3-D conformation of DNA, which influences how genomes are stored, replicated, transcribed, repaired, and many other aspects of DNA activity.

The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA

The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations resulting from mechanical perturbations in cells have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations showing sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulate overextension on different sequences of DNA ((AA)12, (AT)12, (CC)12 and (CG)12) with supercoiling densities at 200 and 50 mM salt concentrations. We find that DNA denatures in the majority of stretching simulations, surprisingly including those with over-twisted DNA. GC-rich sequences are observed to be more stable than AT-rich ones, with the specific response dependent on the base pair order. Furthermore, we find that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (CG)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20-30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.

Sequence-dependent response of DNA to torsional stress: a potential biological regulation mechanism

Torsional restraints on DNA change in time and space during the life of the cell and are an integral part of processes such as gene expression, DNA repair and packaging. The mechanical behavior of DNA under torsional stress has been studied on a mesoscopic scale, but little is known concerning its response at the level of individual base pairs and the effects of base pair composition. To answer this question, we have developed a geometrical restraint that can accurately control the total twist of a DNA segment during all-atom molecular dynamics simulations. By applying this restraint to four different DNA oligomers, we are able to show that DNA responds to both under- and overtwisting in a very heterogeneous manner. Certain base pair steps, in specific sequence environments, are able to absorb most of the torsional stress, leaving other steps close to their relaxed conformation. This heterogeneity also affects the local torsional modulus of DNA. These findings suggest that modifying torsional stress on DNA could act as a modulator for protein binding via the heterogeneous changes in local DNA structure.

Measuring Single-Molecule Twist and Torque in Multiplexed Magnetic Tweezers

Magnetic tweezers permit application of precisely calibrated stretching forces to nucleic acid molecules tethered between a surface and superparamagnetic beads. In addition, magnetic tweezers can control the tethers' twist. Here, we focus on recent extensions of the technique that expand the capabilities of conventional magnetic tweezers by enabling direct measurements of single-molecule torque and twist. Magnetic torque tweezers (MTT) still control the DNA or RNA tether's twist, but directly measure molecular torque by monitoring changes in the equilibrium rotation angle upon overwinding and underwinding of the tether. In freely orbiting magnetic tweezers (FOMT), one end of the tether is allowed to rotate freely, while still applying stretching forces and monitoring rotation angle. Both MTT and FOMT have provided unique insights into the mechanical properties, structural transitions, and interactions of DNA and RNA. Here, we provide step-by-step protocols to carry out FOMT and MTT measurements. In particular, we focus on multiplexed measurements, i.e., measurements that record data for multiple nucleic acid tethers at the same time, to improve statistics and to facilitate the observation of rare events.

Unwinding Induced Melting of Double-Stranded DNA Studied by Free Energy Simulations

DNA unwinding plays a major role in many biological processes, such as replication, transcription, and repair. It can lead to local melting and strand separation and can serve as a key mechanism to promote access to the separate strands of a double-stranded DNA. While DNA unwinding has been investigated extensively by DNA cyclization and single-molecule studies on a length-scale of kilo base pairs, it is neither fully understood at the base pair level nor at the level of molecular interactions. By employing a torque acting on the termini of DNA oligonucleotides during molecular dynamics free energy simulations, we locally unwind the central part of a DNA beyond an elastic (harmonic) regime. The simulations reproduce experimental results on the twist elasticity in the harmonic regime (characterized by a mostly quadratic free energy change with respect to changes in twist) and a deformation up to 7° was found as a limit of the harmonic response. Beyond this limit the free energy increase per twist change dropped dramatically coupled to local base pair disruptions and significant deformation of the nucleic acid backbone structure. Restriction of the DNA bending flexibility resulted in a stiffer harmonic response and an earlier onset of the anharmonic response. Whereas local melting with a complete disruption of base pairing and flipping of nucleotides was observed in case of an AT rich central segment strong backbone changes and changes in the stacking arrangements were observed in case of a GC rich segment. Unrestrained MD simulations starting from locally melted DNA reformed regular B-DNA after 50-300 ns simulation time. The simulations may have important implications for understanding DNA recognition processes coupled with significant structural alterations.

Single-molecule portrait of DNA and RNA double helices

The composition and geometry of the genetic information carriers were described as double-stranded right helices sixty years ago. The flexibility of their sugar-phosphate backbones and the chemistry of their nucleotide subunits, which give rise to the RNA and DNA polymers, were soon reported to generate two main structural duplex states with biological relevance: the so-called A and B forms. Double-stranded (ds) RNA adopts the former whereas dsDNA is stable in the latter. The presence of flexural and torsional stresses in combination with environmental conditions in the cell or in the event of specific sequences in the genome can, however, stabilize other conformations. Single-molecule manipulation, besides affording the investigation of the elastic response of these polymers, can test the stability of their structural states and transition models. This approach is uniquely suited to understanding the basic features of protein binding molecules, the dynamics of molecular motors and to shedding more light on the biological relevance of the information blocks of life. Here, we provide a comprehensive single-molecule analysis of DNA and RNA double helices in the context of their structural polymorphism to set a rigorous interpretation of their material response both inside and outside the cell. From early knowledge of static structures to current dynamic investigations, we review their phase transitions and mechanochemical behaviour and harness this fundamental knowledge not only through biological sciences, but also for Nanotechnology and Nanomedicine.

Investigation of the binding modes between AIE-active molecules and dsDNA by single molecule force spectroscopy

AIE (aggregation-induced emission)-active molecules hold promise for the labeling of biomolecules as well as living cells. The study of the binding modes of such molecules to biomolecules, such as nucleic acids and proteins, will shed light on a deeper understanding of the mechanisms of molecular interactions and eventually facilitate the design/preparation of new AIE-active bioprobes. Herein, we studied the binding modes of double-stranded DNA (dsDNA) with two types of synthetic AIE-active molecules, namely, tetraphenylethene-derived dicationic compounds (cis-TPEDPy and trans-TPEDPy) and anthracene-derived dicationic compounds (DSAI and DSABr-C6) using single molecule force spectroscopy (SMFS) and circular dichroism (CD) spectroscopy. The experimental data indicate that DSAI can strongly intercalate into DNA base pairs, while DSABr-C6 is unable to intercalate into DNA due to the steric hindrance of the alkyl side chains. Cis-TPEDPy and trans-TPEDPy can also intercalate into DNA base pairs, but the binding shows strong ionic strength dependence. Multiple binding modes of TPEDPy with dsDNA have been discussed. In addition, the electrostatic interaction enhanced intercalation of cis-TPEDPy with dsDNA has also been revealed.

E. coli Gyrase Fails to Negatively Supercoil Diaminopurine-Substituted DNA

Type II topoisomerases modify DNA supercoiling, and crystal structures suggest that they sharply bend DNA in the process. Bacterial gyrases are a class of type II topoisomerases that can introduce negative supercoiling by creating a wrap of DNA before strand passage. Isoforms of these essential enzymes were compared to reveal whether they can bend or wrap artificially stiffened DNA. Escherichia coli gyrase and human topoisomerase IIα were challenged with normal DNA or stiffer DNA produced by polymerase chain reaction reactions in which diaminopurine (DAP) replaced adenine deoxyribonucleotide triphosphates. On single DNA molecules twisted with magnetic tweezers to create plectonemes, the rates or pauses during relaxation of positive supercoils in DAP-substituted versus normal DNA were distinct for both enzymes. Gyrase struggled to bend or perhaps open a gap in DAP-substituted DNA, and segments of wider DAP DNA may have fit poorly into the N-gate of the human topoisomerase IIα. Pauses during processive activity on both types of DNA exhibited ATP dependence consistent with two pathways leading to the strand-passage-competent state with a bent gate segment and a transfer segment trapped by an ATP-loaded and latched N-gate. However, E. coli DNA gyrase essentially failed to negatively supercoil 35% stiffer DAP DNA.

Torsionally constrained DNA for single-molecule assays: an efficient, ligation-free method

Controlled twisting of individual, double-stranded DNA molecules provides a unique method to investigate the enzymes that alter DNA topology. Such twisting requires a single DNA molecule to be torsionally constrained. This constraint is achieved by anchoring the opposite ends of the DNA to two separate surfaces via multiple bonds. The traditional protocol for making such DNA involves a three-way ligation followed by gel purification, a laborious process that often leads to low yield both in the amount of DNA and the fraction of molecules that is torsionally constrained. We developed a simple ligation-free procedure for making torsionally constrained DNA via polymerase chain reaction (PCR). This PCR protocol used two 'megaprimers', 400-base-pair long double-stranded DNA that were labelled with either biotin or digoxigenin. We obtained a relatively high yield of gel-purified DNA (∼500 ng/100 µl of PCR reaction). The final construct in this PCR-based method contains only one labelled strand in contrast to the traditional construct in which both strands of the DNA are labelled. Nonetheless, we achieved a high yield (84%) of torsionally constrained DNA when measured using an optical-trap-based DNA-overstretching assay. This protocol significantly simplifies the application and adoption of torsionally constrained assays to a wide range of single-molecule systems.

Surface-dependent mechanical stability of adsorbed human plasma fibronectin on Ti6Al4V: domain unfolding and stepwise unraveling of single compact molecules

In this study, the structure and mechanical stability of human plasma fibronectin (HFN), a major protein component of blood plasma, have been evaluated in detail upon adsorption on the nonirradiated and irradiated Ti6Al4V material through the use of atomic force microscopy. The results indicated that the material surface changes occurring after the irradiation process reduce the disulfide bonds that typically preclude the mechanical denaturation of individual HFN domains and interfere significantly with the intraionic interactions stabilizing the compact conformation of the adsorbed HFN molecules. In particular, upon adsorption on this material, the molecules adopt a more flexible conformation and become mechanically more compliant. Unexpected observations also indicated that, regardless the material surface, a single HFN molecule can be pulled into an extended conformation without the unfolding of its domains through a series of three unraveling steps. The forces involved in the unraveling process were found to be generally lower than the forces required to unfold the individual protein domains. This report is the first one to present the force displacement details associated to the straightening of a single compact protein at the molecular level.

Measuring intermolecular rupture forces with a combined TIRF-optical trap microscope and DNA curtains

We report a new approach to probing DNA-protein interactions by combining optical tweezers with a high-throughput DNA curtains technique. Here we determine the forces required to remove the individual lipid-anchored DNA molecules from the bilayer. We demonstrate that DNA anchored to the bilayer through a single biotin-streptavidin linkage withstands ∼20pN before being pulled free from the bilayer, whereas molecules anchored to the bilayer through multiple attachment points can withstand ⩾65pN; access to this higher force regime is sufficient to probe the responses of protein-DNA interactions to force changes. As a proof-of-principle, we concurrently visualized DNA-bound fluorescently-tagged RNA polymerase while simultaneously stretching the DNA molecules. This work presents a step towards a powerful experimental platform that will enable concurrent visualization of DNA curtains while applying defined forces through optical tweezers.

Bullied no more: when and how DNA shoves proteins around

The predominant protein-centric perspective in protein-DNA-binding studies assumes that the protein drives the interaction. Research focuses on protein structural motifs, electrostatic surfaces and contact potentials, while DNA is often ignored as a passive polymer to be manipulated. Recent studies of DNA topology, the supercoiling, knotting, and linking of the helices, have shown that DNA has the capability to be an active participant in its transactions. DNA topology-induced structural and geometric changes can drive, or at least strongly influence, the interactions between protein and DNA. Deformations of the B-form structure arise from both the considerable elastic energy arising from supercoiling and from the electrostatic energy. Here, we discuss how these energies are harnessed for topology-driven, sequence-specific deformations that can allow DNA to direct its own metabolism.

B-DNA to zip-DNA: simulating a DNA transition to a novel structure with enhanced charge-transport characteristics

The forced extension of a DNA segment is studied in a series of steered molecular dynamics simulations, employing a broad range of pulling forces. Throughout the entire force range, the formation of a zipper-like (zip-) DNA structure is observed. In that structure, first predicted by Lohikoski et al., the bases of the DNA strands interdigitate with each other and form a single-base aromatic stack. Similar motifs, albeit only a few base pairs in extent, have been observed in experimental crystal structures. Analysis of the dynamics of structural changes in pulled DNA shows that S-form DNA, thought to be adopted by DNA under applied force, serves as an intermediate between B-DNA and zip-DNA. Therefore, the phase transition plateau observed in force-extension curves of DNA is suggested to reflect the B-DNA to zip-DNA structural transition. Electronic structure analysis of purine bases in zip-DNA indicates a several-fold to order of magnitude increase in the π-π electronic coupling among nearest-neighbor nucleobases, compared to B-DNA. We further observe that zip-DNA does not require base pair complementarity between DNA strands, and we predict that the increased electronic coupling in zip-DNA will result in a much higher rate of charge transfer through an all-purine zip-DNA compared to B-DNA of equal length.

At the dawn of the 21st century: Is dynamics the missing link for understanding enzyme catalysis?

Enzymes play a key role in almost all biological processes, accelerating a variety of metabolic reactions as well as controlling energy transduction, the transcription, and translation of genetic information, and signaling. They possess the remarkable capacity to accelerate reactions by many orders of magnitude compared to their uncatalyzed counterparts, making feasible crucial processes that would otherwise not occur on biologically relevant timescales. Thus, there is broad interest in understanding the catalytic power of enzymes on a molecular level. Several proposals have been put forward to try to explain this phenomenon, and one that has rapidly gained momentum in recent years is the idea that enzyme dynamics somehow contributes to catalysis. This review examines the dynamical proposal in a critical way, considering basically all reasonable definitions, including (but not limited to) such proposed effects as "coupling between conformational and chemical motions," "landscape searches" and "entropy funnels." It is shown that none of these proposed effects have been experimentally demonstrated to contribute to catalysis, nor are they supported by consistent theoretical studies. On the other hand, it is clarified that careful simulation studies have excluded most (if not all) dynamical proposals. This review places significant emphasis on clarifying the role of logical definitions of different catalytic proposals, and on the need for a clear formulation in terms of the assumed potential surface and reaction coordinate. Finally, it is pointed out that electrostatic preorganization actually accounts for the observed catalytic effects of enzymes, through the corresponding changes in the activation free energies.

Molecular Biomechanics: The Molecular Basis of How Forces Regulate Cellular Function

Recent advances have led to the emergence of molecular biomechanics as an essential element of modern biology. These efforts focus on theoretical and experimental studies of the mechanics of proteins and nucleic acids, and the understanding of the molecular mechanisms of stress transmission, mechanosensing and mechanotransduction in living cells. In particular, single-molecule biomechanics studies of proteins and DNA, and mechanochemical coupling in biomolecular motors have demonstrated the critical importance of molecular mechanics as a new frontier in bioengineering and life sciences. To stimulate a more systematic study of the basic issues in molecular biomechanics, and attract a broader range of researchers to enter this emerging field, here we discuss its significance and relevance, describe the important issues to be addressed and the most critical questions to be answered, summarize both experimental and theoretical/computational challenges, and identify some short-term and long-term goals for the field. The needs to train young researchers in molecular biomechanics with a broader knowledge base, and to bridge and integrate molecular, subcellular and cellular level studies of biomechanics are articulated.

Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

Deforming DNA: from physics to biology

The DNA double helix has become a modern icon which symbolizes our understanding of the molecular basis of life. It is less widely recognized that the double helix proposed by Watson and Crick more than half a century ago is a remarkably adaptable molecule that can undergo major conformational rearrangements without being irreversibly damaged. Indeed, DNA deformation is an intrinsic feature of many of the biological processes in which it is involved. Over the last two decades, single-molecule experiments coupled with molecular modeling have transformed our understanding of DNA flexibility, while the accumulation of high-resolution structures of DNA-protein complexes have demonstrated how organisms can exploit this property as a useful feature for preserving, reading, replicating, and packaging the genetic message. In this Minireview we summarize the information now available on the extreme--and the less extreme--deformations of the double helix.

In the absence of writhe, DNA relieves torsional stress with localized, sequence-dependent structural failure to preserve B-form

To understand how underwinding and overwinding the DNA helix affects its structure, we simulated 19 independent DNA systems with fixed degrees of twist using molecular dynamics in a system that does not allow writhe. Underwinding DNA induced spontaneous, sequence-dependent base flipping and local denaturation, while overwinding DNA induced the formation of Pauling-like DNA (P-DNA). The winding resulted in a bimodal state simultaneously including local structural failure and B-form DNA for both underwinding and extreme overwinding. Our simulations suggest that base flipping and local denaturation may provide a landscape influencing protein recognition of DNA sequence to affect, for examples, replication, transcription and recombination. Additionally, our findings help explain results from single-molecule experiments and demonstrate that elastic rod models are strictly valid on average only for unstressed or overwound DNA up to P-DNA formation. Finally, our data support a model in which base flipping can result from torsional stress.

DNA nanomechanics in the nucleosome

The sequence-dependent mechanics of DNA-histone binding are essential for nucleosome positioning and mobility. Here we reanalyze nucleosome crystal structures in terms of the well-characterized base-pair scale DNA elasticity, extracting the forces and torques acting on all bound DNA base pairs. We find that the strongest forces follow a characteristic repeating pattern that recovers the 12 known DNA backbone-histone contact sites. DNA twist defects and histone point mutations modify this pattern in interpretable ways. Additional, irregular forces between contact sites reveal histone tail-DNA interactions, whereas requiring the absence of external forces leads to a structural refinement of linker DNA. Based on these observations, we propose a simple, structure-based mechanical model of the nucleosome that is able to explain the placement of DNA twist defects in 146 base-pair nucleosomes and allows an estimate of the elastic energy spectrum of nucleosome twist defect states.

The antiparallel loops in gal DNA

Interactions between proteins bound to distant sites along a DNA molecule require bending and twisting deformations in the intervening DNA. In certain systems, the sterically allowed protein-DNA and protein-protein interactions are hypothesized to produce loops with distinct geometries that may also be thermodynamically and biologically distinct. For example, theoretical models of Gal repressor/HU-mediated DNA-looping suggest that the antiparallel DNA loops, A1 and A2, are thermodynamically quite different. They are also biologically different, since in experiments using DNA molecules engineered to form only one of the two loops, the A2 loop failed to repress in vitro transcription. Surprisingly, single molecule measurements show that both loop trajectories form and that they appear to be quite similar energetically and kinetically.

Effect of external stress on the thermal melting of DNA

We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling double-stranded DNA at each end exerts a profound effect on the thermal denaturation, or melting, of a long segment of this molecule. We discuss the effects on this transition of a stretching force applied to opposite ends of the DNA, including full consideration of the consequences of excluded volume, the analysis of which is greatly simplified in this case. We find that in three dimensions the heat capacity acquires a logarithmic dependence on reduced temperature.

Single-molecule atomic force spectroscopy reveals that DnaD forms scaffolds and enhances duplex melting

The Bacillus subtilis DnaD is an essential DNA-binding protein implicated in replication and DNA remodeling. Using single-molecule atomic force spectroscopy, we have studied the interaction of DnaD and its domains with DNA. Our data reveal that binding of DnaD to immobilized single molecules of duplex DNA causes a marked reduction in the 'end-to-end' distance of the DNA in a concentration-dependent manner, consistent with previously reported DnaD-induced looping by scaffold formation. Native DnaD enhances partial melting of the DNA strands. The C-terminal domain (Cd) of DnaD binds to DNA and enhances partial duplex melting but does not cause DNA looping. The Cd-mediated melting is not as efficient as that caused by native DnaD. The N-terminal domain (Nd) does not affect significantly the DNA. A mixture of Nd and Cd fails to recreate the DNA looping effect of native DnaD but produces exactly the same effects as Cd on its own, consistent with the previously reported failure of the separated domains to form DNA-interacting scaffolds.

Molecular Motors: A Theorist's Perspective

Individual molecular motors, or motor proteins, are enzymatic molecules that convert chemical energy, typically obtained from the hydrolysis of ATP (adenosine triphosphate), into mechanical work and motion. Processive motor proteins, such as kinesin, dynein, and certain myosins, step unidirectionally along linear tracks, specifically microtubules and actin filaments, and play a crucial role in cellular transport processes, organization, and function. In this review some theoretical aspects of motor-protein dynamics are presented in the light of current experimental methods that enable the measurement of the biochemical and biomechanical properties on a single-molecule basis. After a brief discussion of continuum ratchet concepts, we focus on discrete kinetic and stochastic models that yield predictions for the mean velocity, V(F, [ATP], ...), and other observables as a function of an imposed load force F, the ATP concentration, and other variables. The combination of appropriate theory with single-molecule observations should help uncover the mechanisms underlying motor-protein function.

Mapping correlated membrane pulsations and fluctuations in human cells

The cell membrane and cytoskeleton are dynamic structures that are strongly influenced by the thermo-mechanical background in addition to biologically driven mechanical processes. We used atomic force microscopy (AFM) to measure the local membrane motion of human foreskin fibroblasts (HFFs) which were found to be governed by random and non-random correlated mechanical processes. Interphase cells displayed distinct membrane pulsations in which the membrane was observed to slowly contract upwards followed by a recovery to its initial position. These pulsations occurred one to three times per minute with variable amplitudes (20-100 pN) separated by periods of random baseline fluctuations with amplitudes of <20 pN. Cells were exposed to actin and microtubule (MT) destabilizing drugs and induced into early apoptosis. Mechanical pulsations (20-80 pN) were not prevented by actin or MT depolymerization but were prevented in early apoptotic cells which only displayed small amplitude baseline fluctuations (<20 pN). Correlation analysis revealed that the cell membrane motion is largely random; however several non-random processes, with time constants varying between approximately 2 and 35 s are present. Results were compared to measured cardiomyocyte motion which was well defined and highly correlated. Employing automated positioning of the AFM tip, interphase HFF correlation time constants were also mapped over a 10 microm2 area above the nucleus providing some insights into the spatial variability of membrane correlations. Here, we are able to show that membrane pulsations and fluctuations can be linked to physiological state and cytoskeletal dynamics through distinct sets of correlation time constants in human cells.

DNA mechanics as a tool to probe helicase and translocase activity

Helicases and translocases are proteins that use the energy derived from ATP hydrolysis to move along or pump nucleic acid substrates. Single molecule manipulation has proved to be a powerful tool to investigate the mechanochemistry of these motors. Here we first describe the basic mechanical properties of DNA unraveled by single molecule manipulation techniques. Then we demonstrate how the knowledge of these properties has been used to design single molecule assays to address the enzymatic mechanisms of different translocases. We report on four single molecule manipulation systems addressing the mechanism of different helicases using specifically designed DNA substrates: UvrD enzyme activity detection on a stretched nicked DNA molecule, HCV NS3 helicase unwinding of a RNA hairpin under tension, the observation of RecBCD helicase/nuclease forward and backward motion, and T7 gp4 helicase mediated opening of a synthetic DNA replication fork. We then discuss experiments on two dsDNA translocases: the RuvAB motor studied on its natural substrate, the Holliday junction, and the chromosome-segregation motor FtsK, showing its unusual coupling to DNA supercoiling.

Modeling DNA loops using the theory of elasticity

An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

Fluctuating enzymes: lessons from single-molecule studies

Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis-Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

Progressing single biomolecule force spectroscopy measurements for the screening of DNA binding agents

Recent studies have indicated that the force-extension properties of single molecules of double stranded (ds) DNA are sensitive to the presence of small molecule DNA binding agents, and also to their mode of binding. These observations raise the possibility of using this approach as a highly sensitive tool for the screening of such agents. However, particularly for studies employing the atomic force microscope (AFM), several non-trivial barriers hinder the progress of this approach to the non-specialist arena and hence also the full realization of this possibility. In this paper, we therefore address a series of key reproducibility and metrological issues associated with this type of measurement. Specifically, we present an improved immobilization method that covalently anchors one end (5' end) of a dual labelled (5'-thiol, 3'-biotin) p53 DNA molecule onto a gold substrate via gold-thiol chemistry, whilst the biotinylated 3' end is available for 'pick-up' using a streptavidin modified AFM tip. We also show that co-surface immobilization of DNA with 6-mercapto-1-hexanol (MCH) can also lead to a further increase the measured contour length. We demonstrate the impact of these improved protocols through the observation of the cooperative transition plateau in a DNA fragment of approximately 118 bp, a significantly smaller fragment than previously investigated. The results of a comparative study of the effects of a model minor groove binder (Hoechst 33258) and an intercalating drug (proflavine), alone, as a mixture and under different buffer conditions, are also presented.

DNA overstretching transition: ionic strength effects

As double-stranded DNA is stretched to its B-form contour length, models of polymer elasticity can describe the dramatic increase in measured force. When the molecule is stretched beyond the contour length, it further shows a highly cooperative overstretching transition. We have developed a theoretical description for this transition by coupling the two-state model and the elasticity theory proposed earlier by others. Furthermore, we have extended this model to account for monovalent salt effects on elastic moduli during the transition. We find that this theoretical description is in very good agreement with recent measurements for the salt dependence of the overstretching transition, allowing us to gain insight into the mechanisms that govern the transition. In double-stranded DNA, the effective length per unit charge varies with salt in agreement with the Manning and Poisson-Boltzmann models for thin polyelectrolyte rods, whereas the other model parameters describing structural features have barely any salt dependence. The results thus suggest that the electrostatic component of force-induced overstretching is mediated mesoscopically via elasticity.

Real-time imaging of DNA ejection from single phage particles

Infection by tailed dsDNA phages is initiated by release of the viral DNA from the capsid and its polarized injection into the host. The driving force for the genome transport remains poorly defined. Among many hypothesis [1], it has been proposed that the internal pressure built up during packaging of the DNA in the capsid is responsible for its injection [2-4]. Whether the energy stored during packaging is sufficient to cause full DNA ejection or only to initiate the process was tested on phage T5 whose DNA (121,400 bp) can be released in vitro by mere interaction of the phage with its E. coli membrane receptor FhuA [5-7]. We present a fluorescence microscopy study investigating in real time the dynamics of DNA ejection from single T5 phages adsorbed onto a microfluidic cell. The ejected DNA was fluorescently stained, and its length was measured at different stages of the ejection after being stretched in a hydrodynamic flow. We conclude that DNA release is not an all-or-none process but occurs in a stepwise fashion and at a rate reaching 75,000 bp/sec. The relevance of this stepwise ejection to the in vivo DNA transfer is discussed.

Dependence of DNA polymerase replication rate on external forces: a model based on molecular dynamics simulations

Molecular dynamics simulations are presented for a Thermus aquaticus (Taq) DNA polymerase I complex (consisting of the protein, the primer-template DNA strands, and the incoming nucleotide) subjected to external forces. The results obtained with a force applied to the DNA template strand provide insights into the effect of the tension on the activity of the enzyme. At forces below 30 pN a local model based on the parameters determined from the simulations, including the restricted motion of the DNA bases at the active site, yields a replication rate dependence on force in agreement with experiment. Simulations above 40 pN reveal large conformational changes in the enzyme-bound DNA that may have a role in the force-induced exonucleolysis observed experimentally.

Structural basis for cooperative DNA binding by CAP and lac repressor

Catabolite gene activator protein (CAP) and lac repressor (LR) are celebrated transcription-regulating proteins that bind to DNA cooperatively forming a ternary complex with the promoter loop. Here we present a multiscale model of the ternary complex derived from crystal structures of the proteins and a continuous structure of the DNA loop built using the theory of elasticity. We predict that the loop is underwound in the binary complex with the LR, whereas in the ternary complex with the LR and CAP, the loop is overwound and extended due to an upstream relocation of a DNA binding hand of LR. The computed relocation distance matches the experimental observations and the energy balance of the system explains the cooperativity effect. Using the multiscale approach, we build an all-atom model of the ternary complex that suggests a series of further experimental investigations.

Modelling DNA loops using continuum and statistical mechanics

The classical Kirchhoff elastic-rod model applied to DNA is extended to account for sequence-dependent intrinsic twist and curvature, anisotropic bending rigidity, electrostatic force interactions, and overdamped Brownian motion in a solvent. The zero-temperature equilibrium rod model is then applied to study the structural basis of the function of the lac repressor protein in the lac operon of Escherichia coli. The structure of a DNA loop induced by the clamping of two distant DNA operator sites by lac repressor is investigated and the optimal geometries for the loop of length 76 bp are predicted. Further, the mimicked binding of catabolite gene activator protein (CAP) inside the loop provides solutions that might explain the experimentally observed synergy in DNA binding between the two proteins. Finally, a combined Monte Carlo and Brownian dynamics solver for a worm-like chain model is described and a preliminary analysis of DNA loop-formation kinetics is presented.

Stretching an adsorbed polymer globule

Using molecular dynamic simulation, we study the stretching of an adsorbed homopolymer in a poor solvent with one end held at a distance ze from the substrate. We measure the vertical force f on the end of the chain as a function of the extension ze and the substrate interaction energy w. The force reaches a plateau value at large extensions. In the strong adsorption limit, we show that the plateau value increases linearly in w in good agreement with a theoretical model. In the weak adsorption limit, a polymer globule with a layered structure is formed and elastically deformed when stretched. In both cases a simple theoretical model permits us to predict the relation between the necessary force to fully detach the polymer and its critical extension.

Promoter unwinding and promoter clearance by RNA polymerase: detection by single-molecule DNA nanomanipulation

By monitoring the end-to-end extension of a mechanically stretched, supercoiled, single DNA molecule, we have been able directly to observe the change in extension associated with unwinding of approximately one turn of promoter DNA by RNA polymerase (RNAP). By performing parallel experiments with negatively and positively supercoiled DNA, we have been able to deconvolute the change in extension caused by RNAP-dependent DNA unwinding (with approximately 1-bp resolution) and the change in extension caused by RNAP-dependent DNA compaction (with approximately 5-nm resolution). We have used this approach to quantify the extent of unwinding and compaction, the kinetics of unwinding and compaction, and effects of supercoiling, sequence, ppGpp, and nucleotides. We also have used this approach to detect promoter clearance and promoter recycling by successive RNAP molecules. We find that the rate of formation and the stability of the unwound complex depend profoundly on supercoiling and that supercoiling exerts its effects mechanically (through torque), and not structurally (through the number and position of supercoils). The approach should permit analysis of other nucleic-acid-processing factors that cause changes in DNA twist and/or DNA compaction.

Stretching and imaging single DNA molecules and chromatin

The advent of single-molecule biology has allowed unprecedented insight into the dynamic behavior of biological macromolecules and their complexes. Unexpected properties, masked by the asynchronous behavior of myriads of molecules in bulk experiments, can be revealed; equally importantly, individual members of a molecular population often exhibit distinct features in their properties. Finally, the single-molecule approaches allow us to study the behavior of biological macromolecules under applied tension or torsion: understanding the mechanical properties of these molecules helps us understand how they function in the cell. The aim of this chapter is to summarize and critically evaluate the properties of single DNA molecules and of single chromatin fibers. The use of the high-resolution imaging capabilities of the atomic force microscopy has been covered, together with manipulating techniques such as optical fibers, optical and magnetic tweezers, and flow fields. We have learned a lot about DNA and how it responds to applied forces. It is also clear that even though the study of the properties of individual chromatin fibers has just begun, the single-molecule approaches are expected to provide a wealth of information concerning the mechanical properties of chromatin and the way its structure changes during processes like transcription and replication.

Chromatin fibers, one-at-a-time

Eukaryotic DNA is presented to the enzymatic machineries that use DNA as a template in the form of chromatin fibers. At the first level of organization, DNA is wrapped around histone octamers to form nucleosomal particles that are connected with stretches of linker DNA; this beads-on-a-string structure folds further to reach a very compact state in the nucleus. Chromatin structure is in constant flux, changing dynamically to accommodate the needs of the cell to replicate, transcribe, and repair the DNA, and to regulate all these processes in time and space. The more conventional biochemical and biophysical techniques used to study chromatin structure and dynamics have been recently complemented by an array of single-molecule approaches, in which chromatin fibers are investigated one-at-a-time. Here we describe single-molecule efforts to see nucleosomes, touch them, put them together, and then take them apart, one-at-a-time. The beginning is exciting and promising, but much more effort will be needed to take advantage of the huge potential that the new physics-based techniques offer.

Localization of denaturation bubbles in random DNA sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to AT-rich segments. In the localized regime, the bubbles exhibit "aging" and move around subdiffusively with continuously varying dynamic exponents. These properties are derived by using results of large-deviation theory together with scaling arguments and are verified by Monte Carlo simulations.

Combined single-molecule force and fluorescence measurements for biology

Recent advances in single-molecule techniques allow the application of force to an individual biomolecule whilst simultaneously monitoring its response using fluorescent probes. The effects of applied mechanical load on single-enzyme turnovers, biomolecular interactions and conformational changes can now be studied with nanometer precision and millisecond time resolution.