First-principles calculation of DNA looping in tethered particle experiments

Conformational properties of hybrid star-shaped polymers comprised of linear and ring arms

We study the influence of arm architecture on the conformational properties of hybrid star-shaped macromolecules called rosette polymers containing linear and ring grafts connected to a central branching point in a good solvent regime. We utilize analytical methods and molecular dynamics simulations to determine the estimates for the relative size ratios of these polymers with respect to linear chains and starlike polymers composed of the same number of solely linear arms and equal molecular weights. The results of numerical simulations corroborate our theoretical prediction that rosette polymers undergo conformational compactification with increasing functionality of grafted rings. Our results quantitatively describe the impact of the complex architecture of the molecules with excluded volume on their effective size measures.

Universal size ratios of Gaussian polymers with complex architecture: radius of gyration vs hydrodynamic radius

We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing [Formula: see text] linear branches and [Formula: see text] closed loops grafted to the central core. We determine size measures such as the gyration radius [Formula: see text] and the hydrodynamic radii [Formula: see text], and obtain the estimates for the size ratio [Formula: see text] with its dependence on the functionality [Formula: see text] of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops [Formula: see text] as compared to linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that [Formula: see text] decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in [Formula: see text] solvents.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

Probing Mitotic CENP-E Kinesin with the Tethered Cargo Motion Assay and Laser Tweezers

Coiled-coil stalks of various kinesins differ significantly in predicted length and structure; this is an adaption that helps these motors carry out their specialized functions. However, little is known about the dynamic stalk configuration in moving motors. To gain insight into the conformational properties of the transporting motors, we developed a theoretical model to predict Brownian motion of a microbead tethered to the tail of a single, freely walking molecule. This approach, which we call the tethered cargo motion (TCM) assay, provides an accurate measure of the mechanical properties of motor-cargo tethering, verified using kinesin-1 conjugated to a microbead via DNA links in vitro. Applying the TCM assay to the mitotic kinesin CENP-E unexpectedly revealed that when walking along a microtubule track, this highly elongated molecule with a contour length of 230 nm formed a 20-nm-long tether. The stalk of a walking CENP-E could not be extended fully by application of sideways force with optical tweezers (up to 4 pN), implying that CENP-E carries its cargo in a compact configuration. Assisting force applied along the microtubule track accelerates CENP-E walking, but this increase does not depend on the presence of the CENP-E stalk. Our results suggest that the unusually large stalk of CENP-E has little role in regulating its function as a transporter. The adjustable stalk configuration may represent a regulatory mechanism for controlling the physical reach between kinetochore-bound CENP-E and spindle microtubules, or it may assist localizing various kinetochore regulators in the immediate vicinity of the kinetochore-embedded microtubule ends. The TCM assay and underlying theoretical framework will provide a general guide for determining the dynamic configurations of various molecular motors moving along their tracks, freely or under force.

Swi5-Sfr1 stimulates Rad51 recombinase filament assembly by modulating Rad51 dissociation

Eukaryotic Rad51 protein is essential for homologous-recombination repair of DNA double-strand breaks. Rad51 recombinases first assemble onto single-stranded DNA to form a nucleoprotein filament, required for function in homology pairing and strand exchange. This filament assembly is the first regulation step in homologous recombination. Rad51 nucleation is kinetically slow, and several accessory factors have been identified to regulate this step. Swi5-Sfr1 (S5S1) stimulates Rad51-mediated homologous recombination by stabilizing Rad51 nucleoprotein filaments, but the mechanism of stabilization is unclear. We used single-molecule tethered particle motion experiments to show that mouse S5S1 (mS5S1) efficiently stimulates mouse RAD51 (mRAD51) nucleus formation and inhibits mRAD51 dissociation from filaments. We also used single-molecule fluorescence resonance energy transfer experiments to show that mS5S1 promotes stable nucleus formation by specifically preventing mRAD51 dissociation. This leads to a reduction of nucleation size from three mRAD51 to two mRAD51 molecules in the presence of mS5S1. Compared with mRAD51, fission yeast Rad51 (SpRad51) exhibits fast nucleation but quickly dissociates from the filament. SpS5S1 specifically reduces SpRad51 disassembly to maintain a stable filament. These results clearly demonstrate the conserved function of S5S1 by primarily stabilizing Rad51 on DNA, allowing both the formation of the stable nucleus and the maintenance of filament length.

Universal size properties of a star-ring polymer structure in disordered environments

We consider the complex polymer system, consisting of a ring polymer connected to the f_{1}-branched starlike structure, in a good solvent in the presence of structural inhomogeneities. In particular cases f_{1}=1 and f_{1}=2, such a system restores the synthesized tadpole-shaped polystyrenes [Doi et al., Macromolecules 46, 1075 (2013)MAMOBX0024-929710.1021/ma302511j]. We assume that structural defects are correlated at large distances x according to a power law x^{-a}. Applying the direct polymer renormalization approach, we evaluate the universal size characteristics such as the ratio of the radii of gyration of star-ring and star topologies, and compare the effective sizes of single arms in complex structures and isolated polymers of the same total molecular weight. The nontrivial impact of disorder on these quantities is analyzed.

Quantifying the impact of simple DNA parameters on the cyclization J-factor for single-basepair-addition families

We use Monte Carlo simulation to quantify the change in cyclization J-factor within a dramatically simplified model of DNA that involves parameters for uniform stiffnesses, intrinsic twist, and intrinsic bending (including nonplanar bending). Plots of J versus DNA length over multiple periods of helical repeat are fit to a simple functional form in order to project the behavior of J over a broad range of these model parameters. In some instances, this process allows us to find families of DNA molecules (within our model) with quite different material properties, but very similar plots of J versus length, so similar as to likely to be indistinguishable by experiments. This effect is seen both for the parameter-pair of bend angle and stiffness scaling, as well as for the parameter-trio of helical repeat, bend angle, and bend non-planarity.

Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors

Tethered Particle Motion (TPM) is a versatile in vitro technique for monitoring the conformations a linear macromolecule, such as DNA, can exhibit. The technique involves monitoring the diffusive motion of a particle anchored to a fixed point via the macromolecule of interest, which acts as a tether. In this chapter, we provide an overview of TPM, review the fundamental principles that determine the accuracy with which effective tether lengths can be used to distinguish different tether conformations, present software tools that assist in capturing and analyzing TPM data, and provide a protocol which uses TPM to characterize lac repressor-induced DNA looping. Critical to any TPM assay is the understanding of the timescale over which the diffusive motion of the particle must be observed to accurately distinguish tether conformations. Approximating the tether as a Hookean spring, we show how to estimate the diffusion timescale and discuss how it relates to the confidence with which tether conformations can be distinguished. Applying those estimates to a lac repressor titration assay, we describe how to perform a TPM experiment. We also provide graphically driven software which can be used to speed up data collection and analysis. Lastly, we detail how TPM data from the titration assay can be used to calculate relevant molecular descriptors such as the J factor for DNA looping and lac repressor-operator dissociation constants. While the included protocol is geared toward studying DNA looping, the technique, fundamental principles, and analytical methods are more general and can be adapted to a wide variety of molecular systems.

Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius

Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.

Extreme bendability of DNA double helix due to bending asymmetry

Experimental data of the DNA cyclization (J-factor) at short length scales exceed the theoretical expectation based on the wormlike chain (WLC) model by several orders of magnitude. Here, we propose that asymmetric bending rigidity of the double helix in the groove direction can be responsible for extreme bendability of DNA at short length scales and it also facilitates DNA loop formation at these lengths. To account for the bending asymmetry, we consider the asymmetric elastic rod (AER) model which has been introduced and parametrized in an earlier study [B. Eslami-Mossallam and M. R. Ejtehadi, Phys. Rev. E 80, 011919 (2009)]. Exploiting a coarse grained representation of the DNA molecule at base pair (bp) level and using the Monte Carlo simulation method in combination with the umbrella sampling technique, we calculate the loop formation probability of DNA in the AER model. We show that the DNA molecule has a larger J-factor compared to the WLC model which is in excellent agreement with recent experimental data.

Interplay of Protein Binding Interactions, DNA Mechanics, and Entropy in DNA Looping Kinetics

DNA looping plays a key role in many fundamental biological processes, including gene regulation, recombination, and chromosomal organization. The looping of DNA is often mediated by proteins whose structural features and physical interactions can alter the length scale at which the looping occurs. Looping and unlooping processes are controlled by thermodynamic contributions associated with mechanical deformation of the DNA strand and entropy arising from thermal fluctuations of the conformation. To determine how these confounding effects influence DNA looping and unlooping kinetics, we present a theoretical model that incorporates the role of the protein interactions, DNA mechanics, and conformational entropy. We show that for shorter DNA strands the interaction distance affects the transition state, resulting in a complex relationship between the looped and unlooped state lifetimes and the physical properties of the looped DNA. We explore the range of behaviors that arise with varying interaction distance and DNA length. These results demonstrate how DNA deformation and entropy dictate the scaling of the looping and unlooping kinetics versus the J-factor, establishing the connection between kinetic and equilibrium behaviors. Our results show how the twist-and-bend elasticity of the DNA chain modulates the kinetics and how the influence of the interaction distance fades away at intermediate to longer chain lengths, in agreement with previous scaling predictions.

Loop statistics in polymers in crowded environment

We analyze the probability to find a single loop in a long flexible polymer chain in disordered environment in d dimensions. The structural defects are considered to be correlated on large distances r according to a power law ∼r(-a). Working within the frames of continuous chain model and applying the direct polymer renormalization scheme, we obtain the values of critical exponents governing the scaling of probabilities to find the loops of various positions along the chain as function of loops' length. Our results quantitatively reveal that the presence of structural defects in environment decreases the probability of loop formation in polymer macromolecules.

DNA topology confers sequence specificity to nonspecific architectural proteins

Topological constraints placed on short fragments of DNA change the disorder found in chain molecules randomly decorated by nonspecific, architectural proteins into tightly organized 3D structures. The bacterial heat-unstable (HU) protein builds up, counter to expectations, in greater quantities and at particular sites along simulated DNA minicircles and loops. Moreover, the placement of HU along loops with the "wild-type" spacing found in the Escherichia coli lactose (lac) and galactose (gal) operons precludes access to key recognition elements on DNA. The HU protein introduces a unique spatial pathway in the DNA upon closure. The many ways in which the protein induces nearly the same closed circular configuration point to the statistical advantage of its nonspecificity. The rotational settings imposed on DNA by the repressor proteins, by contrast, introduce sequential specificity in HU placement, with the nonspecific protein accumulating at particular loci on the constrained duplex. Thus, an architectural protein with no discernible DNA sequence-recognizing features becomes site-specific and potentially assumes a functional role upon loop formation. The locations of HU on the closed DNA reflect long-range mechanical correlations. The protein responds to DNA shape and deformability—the stiff, naturally straight double-helical structure—rather than to the unique features of the constituent base pairs. The structures of the simulated loops suggest that HU architecture, like nucleosomal architecture, which modulates the ability of regulatory proteins to recognize their binding sites in the context of chromatin, may influence repressor-operator interactions in the context of the bacterial nucleoid.

Enhanced tethered-particle motion analysis reveals viscous effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl2 or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.

Multiple LacI-mediated loops revealed by Bayesian statistics and tethered particle motion

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple coexisting loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e. DNA–protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA-binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein–nucleic acid interactions.

Lac repressor mediated DNA looping: Monte Carlo simulation of constrained DNA molecules complemented with current experimental results

Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor.

Bacterial promoter repression by DNA looping without protein-protein binding competition

The Escherichia coli lactose operon provides a paradigm for understanding gene control by DNA looping where the lac repressor (LacI) protein competes with RNA polymerase for DNA binding. Not all promoter loops involve direct competition between repressor and RNA polymerase. This raises the possibility that positioning a promoter within a tightly constrained DNA loop is repressive per se, an idea that has previously only been considered in vitro. Here, we engineer living E. coli bacteria to measure repression due to promoter positioning within such a tightly constrained DNA loop in the absence of protein–protein binding competition. We show that promoters held within such DNA loops are repressed ∼100-fold, with up to an additional ∼10-fold repression (∼1000-fold total) dependent on topological positioning of the promoter on the inner or outer face of the DNA loop. Chromatin immunoprecipitation data suggest that repression involves inhibition of both RNA polymerase initiation and elongation. These in vivo results show that gene repression can result from tightly looping promoter DNA even in the absence of direct competition between repressor and RNA polymerase binding.

Mathematical model of alternative mechanism of telomere length maintenance

Biopolymer length regulation is a complex process that involves a large number of biological, chemical, and physical subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres-nucleoprotein structures at the ends of linear chromosomes consisting of tandemly repeated DNA sequences and a specialized set of proteins. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination. Various linear and circular DNA structures were identified to participate in ALT, however, dynamics of the whole process is still poorly understood. We propose a chemical kinetics model of ALT with kinetic rates systematically derived from the biophysics of DNA diffusion and looping. The reaction system is reduced to a coagulation-fragmentation system by quasi-steady-state approximation. The detailed treatment of kinetic rates yields explicit formulas for expected size distributions of telomeres that demonstrate the key role played by the J factor, a quantitative measure of bending of polymers. The results are in agreement with experimental data and point out interesting phenomena: an appearance of very long telomeric circles if the total telomere density exceeds a critical value (excess mass) and a nonlinear response of the telomere size distributions to the amount of telomeric DNA in the system. The results can be of general importance for understanding dynamics of telomeres in telomerase-independent systems as this mode of telomere maintenance is similar to the situation in tumor cells lacking telomerase activity. Furthermore, due to its universality, the model may also serve as a prototype of an interaction between linear and circular DNA structures in various settings.

DNA sequence-dependent mechanics and protein-assisted bending in repressor-mediated loop formation

As the chief informational molecule of life, DNA is subject to extensive physical manipulations. The energy required to deform double-helical DNA depends on sequence, and this mechanical code of DNA influences gene regulation, such as through nucleosome positioning. Here we examine the sequence-dependent flexibility of DNA in bacterial transcription factor-mediated looping, a context for which the role of sequence remains poorly understood. Using a suite of synthetic constructs repressed by the Lac repressor and two well-known sequences that show large flexibility differences in vitro, we make precise statistical mechanical predictions as to how DNA sequence influences loop formation and test these predictions using in vivo transcription and in vitro single-molecule assays. Surprisingly, sequence-dependent flexibility does not affect in vivo gene regulation. By theoretically and experimentally quantifying the relative contributions of sequence and the DNA-bending protein HU to DNA mechanical properties, we reveal that bending by HU dominates DNA mechanics and masks intrinsic sequence-dependent flexibility. Such a quantitative understanding of how mechanical regulatory information is encoded in the genome will be a key step towards a predictive understanding of gene regulation at single-base pair resolution.

Poly(dA:dT)-rich DNAs are highly flexible in the context of DNA looping

Large-scale DNA deformation is ubiquitous in transcriptional regulation in prokaryotes and eukaryotes alike. Though much is known about how transcription factors and constellations of binding sites dictate where and how gene regulation will occur, less is known about the role played by the intervening DNA. In this work we explore the effect of sequence flexibility on transcription factor-mediated DNA looping, by drawing on sequences identified in nucleosome formation and ligase-mediated cyclization assays as being especially favorable for or resistant to large deformations. We examine a poly(dA:dT)-rich, nucleosome-repelling sequence that is often thought to belong to a class of highly inflexible DNAs; two strong nucleosome positioning sequences that share a set of particular sequence features common to nucleosome-preferring DNAs; and a CG-rich sequence representative of high G+C-content genomic regions that correlate with high nucleosome occupancy in vivo. To measure the flexibility of these sequences in the context of DNA looping, we combine the in vitro single-molecule tethered particle motion assay, a canonical looping protein, and a statistical mechanical model that allows us to quantitatively relate the looping probability to the looping free energy. We show that, in contrast to the case of nucleosome occupancy, G+C content does not positively correlate with looping probability, and that despite sharing sequence features that are thought to determine nucleosome affinity, the two strong nucleosome positioning sequences behave markedly dissimilarly in the context of looping. Most surprisingly, the poly(dA:dT)-rich DNA that is often characterized as highly inflexible in fact exhibits one of the highest propensities for looping that we have measured. These results argue for a need to revisit our understanding of the mechanical properties of DNA in a way that will provide a basis for understanding DNA deformation over the entire range of biologically relevant scenarios that are impacted by DNA deformability.

Interplay of protein and DNA structure revealed in simulations of the lac operon

The E. coli Lac repressor is the classic textbook example of a protein that attaches to widely spaced sites along a genome and forces the intervening DNA into a loop. The short loops implicated in the regulation of the lac operon suggest the involvement of factors other than DNA and repressor in gene control. The molecular simulations presented here examine two likely structural contributions to the in-vivo looping of bacterial DNA: the distortions of the double helix introduced upon association of the highly abundant, nonspecific nucleoid protein HU and the large-scale deformations of the repressor detected in low-resolution experiments. The computations take account of the three-dimensional arrangements of nucleotides and amino acids found in crystal structures of DNA with the two proteins, the natural rest state and deformational properties of protein-free DNA, and the constraints on looping imposed by the conformation of the repressor and the orientation of bound DNA. The predicted looping propensities capture the complex, chain-length-dependent variation in repression efficacy extracted from gene expression studies and in vitro experiments and reveal unexpected chain-length-dependent variations in the uptake of HU, the deformation of repressor, and the folding of DNA. Both the opening of repressor and the presence of HU, at levels approximating those found in vivo, enhance the probability of loop formation. HU affects the global organization of the repressor and the opening of repressor influences the levels of HU binding to DNA. The length of the loop determines whether the DNA adopts antiparallel or parallel orientations on the repressor, whether the repressor is opened or closed, and how many HU molecules bind to the loop. The collective behavior of proteins and DNA is greater than the sum of the parts and hints of ways in which multiple proteins may coordinate the packaging and processing of genetic information.

Nanocarrier Hydrodynamics and Binding in Targeted Drug Delivery: Challenges in Numerical Modeling and Experimental Validation

This review discusses current progress and future challenges in the numerical modeling of targeted drug delivery using functionalized nanocarriers (NC). Antibody coated nanocarriers of various size and shapes, also called functionalized nanocarriers, are designed to be injected in the vasculature, whereby they undergo translational and rotational motion governed by hydrodynamic interaction with blood particulates as well as adhesive interactions mediated by the surface antibody binding to target antigens/receptors on cell surfaces. We review current multiscale modeling approaches rooted in computational fluid dynamics and nonequilibrium statistical mechanics to accurately resolve fluid, thermal, as well as adhesive interactions governing nanocarrier motion and their binding to endothelial cells lining the vasculature. We also outline current challenges and unresolved issues surrounding the modeling methods. Experimental approaches in pharmacology and bioengineering are discussed briefly from the perspective of model validation.

DNA looping in prokaryotes: experimental and theoretical approaches

Transcriptional regulation is at the heart of biological functions such as adaptation to a changing environment or to new carbon sources. One of the mechanisms which has been found to modulate transcription, either positively (activation) or negatively (repression), involves the formation of DNA loops. A DNA loop occurs when a protein or a complex of proteins simultaneously binds to two different sites on DNA with looping out of the intervening DNA. This simple mechanism is central to the regulation of several operons in the genome of the bacterium Escherichia coli, like the lac operon, one of the paradigms of genetic regulation. The aim of this review is to gather and discuss concepts and ideas from experimental biology and theoretical physics concerning DNA looping in genetic regulation. We first describe experimental techniques designed to show the formation of a DNA loop. We then present the benefits that can or could be derived from a mechanism involving DNA looping. Some of these are already experimentally proven, but others are theoretical predictions and merit experimental investigation. Then, we try to identify other genetic systems that could be regulated by a DNA looping mechanism in the genome of Escherichia coli. We found many operons that, according to our set of criteria, have a good chance to be regulated with a DNA loop. Finally, we discuss the proposition recently made by both biologists and physicists that this mechanism could also act at the genomic scale and play a crucial role in the spatial organization of genomes.

Definition of the persistence length in the coarse-grained models of DNA elasticity

By considering the detailed structure of DNA in the base pair level, two possible definitions of the persistence length are compared. One definition is related to the orientation of the terminal base pairs, and the other is based on the vectors which connect two adjacent base pairs at each end of the molecule. It is shown that although these definitions approach each other for long DNA molecules, they are dramatically different on short length scales. We show analytically that the difference mostly comes from the shear flexibility of the molecule and can be used to measure the shear modulus of DNA.

Extreme bendability of DNA less than 100 base pairs long revealed by single-molecule cyclization

The classical view of DNA posits that DNA must be stiff below the persistence length [<150 base pairs (bp)], but recent studies addressing this have yielded contradictory results. We developed a fluorescence-based, protein-free assay for studying the cyclization of single DNA molecules in real time. The assay samples the equilibrium population of a sharply bent, transient species that is entirely suppressed in single-molecule mechanical measurements and is biologically more relevant than the annealed species sampled in the traditional ligase-based assay. The looping rate has a weak length dependence between 67 and 106 bp that cannot be described by the worm-like chain model. Many biologically important protein-DNA interactions that involve looping and bending of DNA below 100 bp likely use this intrinsic bendability of DNA.

Sequence dependence of transcription factor-mediated DNA looping

DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes and DNA looping in transcriptional regulation in both prokaryotes and eukaryotes. These kinds of regulatory problems are now becoming amenable to systematic quantitative dissection with a powerful dialogue between theory and experiment. Here, we use a single-molecule experiment in conjunction with a statistical mechanical model to test quantitative predictions for the behavior of DNA looping at short length scales and to determine how DNA sequence affects looping at these lengths. We calculate and measure how such looping depends upon four key biological parameters: the strength of the transcription factor binding sites, the concentration of the transcription factor, and the length and sequence of the DNA loop. Our studies lead to the surprising insight that sequences that are thought to be especially favorable for nucleosome formation because of high flexibility lead to no systematically detectable effect of sequence on looping, and begin to provide a picture of the distinctions between the short length scale mechanics of nucleosome formation and looping.

High density single-molecule-bead arrays for parallel single molecule force spectroscopy

The assembly of a highly parallel force spectroscopy tool requires careful placement of single-molecule targets on the substrate and the deliberate manipulation of a multitude of force probes. Since the probe must approach the target biomolecule for covalent attachment, while avoiding irreversible adhesion to the substrate, the use of polymer microspheres as force probes to create the tethered bead array poses a problem. Therefore, the interactions between the force probe and the surface must be repulsive at very short distances (<5 nm) and attractive at long distances. To achieve this balance, the chemistry of the substrate, force probe, and solution must be tailored to control the probe-surface interactions. In addition to an appropriately designed chemistry, it is necessary to control the surface density of the target molecule in order to ensure that only one molecule is interrogated by a single force probe. We used gold-thiol chemistry to control both the substrate's surface chemistry and the spacing of the studied molecules, through binding of the thiol-terminated DNA and an inert thiol forming a blocking layer. For our single molecule array, we modeled the forces between the probe and the substrate using DLVO theory and measured their magnitude and direction with colloidal probe microscopy. The practicality of each system was tested using a probe binding assay to evaluate the proportion of the beads remaining adhered to the surface after application of force. We have translated the results specific for our system to general guiding principles for preparation of tethered bead arrays and demonstrated the ability of this system to produce a high yield of active force spectroscopy probes in a microwell substrate. This study outlines the characteristics of the chemistry needed to create such a force spectroscopy array.

DNA looping by FokI: the impact of twisting and bending rigidity on protein-induced looping dynamics

Protein-induced DNA looping is crucial for many genetic processes such as transcription, gene regulation and DNA replication. Here, we use tethered-particle motion to examine the impact of DNA bending and twisting rigidity on loop capture and release, using the restriction endonuclease FokI as a test system. To cleave DNA efficiently, FokI bridges two copies of an asymmetric sequence, invariably aligning the sites in parallel. On account of the fixed alignment, the topology of the DNA loop is set by the orientation of the sites along the DNA. We show that both the separation of the FokI sites and their orientation, altering, respectively, the twisting and the bending of the DNA needed to juxtapose the sites, have profound effects on the dynamics of the looping interaction. Surprisingly, the presence of a nick within the loop does not affect the observed rigidity of the DNA. In contrast, the introduction of a 4-nt gap fully relaxes all of the torque present in the system but does not necessarily enhance loop stability. FokI therefore employs torque to stabilise its DNA-looping interaction by acting as a ‘torsional’ catch bond.

Probing DNA topology using tethered particle motion

Transcription factors mediate the formation of nucleoprotein complexes that are critical for efficient regulation of epigenetic switches. In these complexes, DNA is frequently bent or looped by the protein; other times, strong interactions lead the DNA to fully wrap the regulatory protein(s). The equilibrium between the bending, looping, full and partial wrapping of DNA governs the level of transcriptional regulation and is tuned by biophysical parameters. Characterization of the structure, kinetics, and thermodynamics of formation of such nucleoprotein complexes is fundamental to the understanding of the molecular mechanisms that underlie the operation of the genetic switches controlled by them. Here, we describe in detail how to perform tethered particle motion experiments aimed at understanding how protein-DNA interactions influence the formation and breakdown of these regulatory complexes.

DNA modeling reveals an extended lac repressor conformation in classic in vitro binding assays

Protein-mediated DNA looping, such as that induced by the lactose repressor (LacI) of Escherichia coli, is a well-known gene regulation mechanism. Although researchers have given considerable attention to DNA looping by LacI, many unanswered questions about this mechanism, including the role of protein flexibility, remain. Recent single-molecule observations suggest that the two DNA-binding domains of LacI are capable of splaying open about the tetramerization domain into an extended conformation. We hypothesized that if recent experiments were able to reveal the extended conformation, it is possible that such structures occurred in previous studies as well. In this study, we tested our hypothesis by reevaluating two classic in vitro binding assays using a computational rod model of DNA. The experiments and computations evaluate the looping of both linear DNA and supercoiled DNA minicircles over a broad range of DNA interoperator lengths. The computed energetic minima align well with the experimentally observed interoperator length for optimal loop stability. Of equal importance, the model reveals that the most stable loops for linear DNA occur when LacI adopts the extended conformation. In contrast, for DNA minicircles, optimal stability may arise from either the closed or the extended protein conformation depending on the degree of supercoiling and the interoperator length.

Building enhancers from the ground up: a synthetic biology approach

A challenge of the synthetic biology approach is to use our understanding of a system to recreate a biological function with specific properties. We have applied this framework to bacterial enhancers, combining a driver, transcription factor binding sites, and a poised polymerase to create synthetic modular enhancers. Our findings suggest that enhancer-based transcriptional control depends critically and quantitatively on DNA looping, leading to complex regulatory effects when the enhancer cassettes contain additional transcription factor binding sites for TetR, a bacterial transcription factor. We show through a systematic interplay of experiment and thermodynamic modeling that the level of gene expression can be modulated to convert a variable inducer concentration input into discrete or step-like output expression levels. Finally, using a different DNA-binding protein (TraR), we show that the regulatory output is not a particular feature of the specific DNA-binding protein used for the enhancer but a general property of synthetic bacterial enhancers.

Contribution of nonlocal interactions to DNA elasticity

A nonlocal harmonic elastic rod model is proposed to describe the elastic behavior of short DNA molecules. We show that the nonlocal interactions contribute to effective bending energy of the molecule and affect its apparent persistence length. It is also shown that the anomalous behavior which has been observed in all-atom molecular dynamic simulations [A. K. Mazur, Biophys. J. 134, 4507 (2006)] can be a consequence of both nonlocal interactions between DNA base pairs and the intrinsic curvature of DNA.

Quantitative High-Resolution Sensing of DNA Hybridization Using Magnetic Tweezers with Evanescent Illumination

We applied the combined approach of evanescent nanometry and force spectroscopy using magnetic tweezers to quantify the degree of hybridization of a single synthetic single-stranded DNA oligomer to a resolution approaching a single-base. In this setup, the 200 nucleotide long DNA was covalently attached to the surface of an optically transparent solid support at one end and to the surface of a superparamagnetic fluorescent microsphere (force probe) at the other end. The force was applied to the probes using an electromagnet. The end-to-end molecular distance (i.e. out-of-image-plane position of the force probe) was determined from the intensity of the probe fluorescent image observed with total-internal reflectance microscopy. An equation of state for single stranded DNA molecules under tension (extensible freely jointed chain) was used to derive the penetration depth of the evanescent field and to calibrate the magnetic properties of the force probes. The parameters of the magnetic response of the force probes obtained from the equation of state remained constant when changing the penetration depth, indicating a robust calibration procedure. The results of such a calibration were also confirmed using independently measured probe-surface distances for probes mounted onto cantilevers of an atomic force microscope. Upon hybridization of the complementary 50 nucleotide-long oligomer to the surface-bound 200-mer, the changes in the force-distance curves were consistent with the quantitative conversion of 25% of the original single-stranded DNA to its double-stranded form, which was modeled as an elastic rod. The method presented here for quantifying the hybridization state of the single DNA molecules has potential for determining the degree of hybridization of individual molecules in a single molecule array with high accuracy.

Comparison of Brownian-dynamics-based estimates of polymer tension with direct force measurements

With the aid of brownian dynamics models, it is possible to estimate polymer tension by monitoring polymers' transverse thermal fluctuations. To assess the precision of the approach, brownian dynamics-based tension estimates were compared with the force applied to rhodamine-phalloidin labeled actin filaments bound to polymer beads and suspended between two optical traps. The transverse thermal fluctuations of each filament were monitored with a CCD camera, and the images were analyzed to obtain the filament's transverse displacement variance as a function of position along the filament, the filament's tension, and the camera's exposure time. A linear Brownian dynamics model was used to estimate the filament's tension. The estimated force was compared and agreed within 30% (when the tension <0.1 pN ) and 70% (when the tension <1 pN ) with the applied trap force. In addition, the paper presents concise asymptotic expressions for the mechanical compliance of a system consisting of a filament attached tangentially to bead handles (dumbbell system). The techniques described here can be used for noncontact estimates of polymers' and fibers' tension.

Quantification of the physiochemical constraints on the export of spider silk proteins by Salmonella type III secretion

Background

The type III secretion system (T3SS) is a molecular machine in gram negative bacteria that exports proteins through both membranes to the extracellular environment. It has been previously demonstrated that the T3SS encoded in Salmonella Pathogenicity Island 1 (SPI-1) can be harnessed to export recombinant proteins. Here, we demonstrate the secretion of a variety of unfolded spider silk proteins and use these data to quantify the constraints of this system with respect to the export of recombinant protein.

Results

To test how the timing and level of protein expression affects secretion, we designed a hybrid promoter that combines an IPTG-inducible system with a natural genetic circuit that controls effector expression in Salmonella (psicA). LacO operators are placed in various locations in the psicA promoter and the optimal induction occurs when a single operator is placed at the +5nt (234-fold) and a lower basal level of expression is achieved when a second operator is placed at -63nt to take advantage of DNA looping. Using this tool, we find that the secretion efficiency (protein secreted divided by total expressed) is constant as a function of total expressed. We also demonstrate that the secretion flux peaks at 8 hours. We then use whole gene DNA synthesis to construct codon optimized spider silk genes for full-length (3129 amino acids) Latrodectus hesperus dragline silk, Bombyx mori cocoon silk, and Nephila clavipes flagelliform silk and PCR is used to create eight truncations of these genes. These proteins are all unfolded polypeptides and they encompass a variety of length, charge, and amino acid compositions. We find those proteins fewer than 550 amino acids reliably secrete and the probability declines significantly after ~700 amino acids. There also is a charge optimum at -2.4, and secretion efficiency declines for very positively or negatively charged proteins. There is no significant correlation with hydrophobicity.

Conclusions

We show that the natural system encoded in SPI-1 only produces high titers of secreted protein for 4-8 hours when the natural psicA promoter is used to drive expression. Secretion efficiency can be high, but declines for charged or large sequences. A quantitative characterization of these constraints will facilitate the effective use and engineering of this system.

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.

Towards building a chromosome segregation machine

All organisms, from bacteria to humans, face the daunting task of replicating, packaging and segregating up to two metres (about 6 x 10(9) base pairs) of DNA when each cell divides. This task is carried out up to a trillion times during the development of a human from a single fertilized cell. The strategy by which DNA is replicated is now well understood. But when it comes to packaging and segregating a genome, the mechanisms are only beginning to be understood and are often as variable as the organisms in which they are studied.

Femtonewton entropic forces can control the formation of protein-mediated DNA loops

We show that minuscule entropic forces, on the order of 100 fN, can prevent the formation of DNA loops-a ubiquitous means of regulating the expression of genes. We observe a tenfold decrease in the rate of LacI-mediated DNA loop formation when a tension of 200 fN is applied to the substrate DNA, biasing the thermal fluctuations that drive loop formation and breakdown events. Conversely, once looped, the DNA-protein complex is insensitive to applied force. Our measurements are in excellent agreement with a simple polymer model of loop formation in DNA, and show that an antiparallel topology is the preferred LacI-DNA loop conformation for a generic loop-forming construct.

Tetramer opening in LacI-mediated DNA looping

Lactose repressor protein (LacI) controls transcription of the genes involved in lactose metabolism in bacteria. Essential to optimal LacI-mediated regulation is its ability to bind simultaneously to two operators, forming a loop on the intervening DNA. Recently, several lines of evidence (both theoretical and experimental) have suggested various possible loop structures associated with different DNA binding topologies and LacI tetramer structural conformations (adopted by flexing about the C-terminal tetramerization domain). We address, specifically, the role of protein opening in loop formation by employing the single-molecule tethered particle motion method on LacI protein mutants chemically cross-linked at different positions along the cleft between the two dimers. Measurements on the wild-type and uncross-linked LacI mutants led to the observation of two distinct levels of short tether length, associated with two different DNA looping structures. Restricting conformational flexibility of the protein by chemical cross-linking induces pronounced effects. Crosslinking the dimers at the level of the N-terminal DNA binding head (E36C) completely suppresses looping, whereas cross-linking near the C-terminal tetramerization domain (Q231C) results in changes of looping geometry detected by the measured tether length distributions. These observations lead to the conclusion that tetramer opening plays a definite role in at least a subset of LacI/DNA loop conformations.

Concentration and length dependence of DNA looping in transcriptional regulation

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.