A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

Conformation of ring single-stranded DNA measured by DNA origami structures

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a complex challenge that has been addressed lately by different methods. We measured the persistence length of ring ssDNA using a combination of a special DNA origami structure, a self-avoiding ring polymer simulation model, and nonparametric estimation statistics. The method overcomes the complexities set forth by previously used methods. We designed the DNA origami nano structures and measured the ring ssDNA polymer conformations using atomic force microscopy. We then calculated their radius of gyration, which was used as a fitting parameter for finding the persistence length. As there is no simple formulation for the radius of gyration distribution, we developed a simulation program consisting of a self-avoiding ring polymer to fit the persistence length to the experimental data. ssDNA naturally forms stem-loops, which should be taken into account in fitting a model to the experimental measurement. To overcome that hurdle, we found the possible loops using minimal energy considerations and used them in our fitting procedure of the persistence length. Due to the statistical nature of the loops formation, we calculated the persistence length for different percentages of loops that are formed. In the range of 25–75% loop formation, we found the persistence length to be 1.9–4.4 nm, and for 50% loop formation we get a persistence length of 2.83 ± 0.63 nm. This estimation narrows the previously known persistence length and provides tools for finding the conformations of ssDNA.     

Role of the closing base pair for d(GCA) hairpin stability: free energy analysis and folding simulations

Hairpin loops belong to the most important structural motifs in folded nucleic acids. The d(GNA) sequence in DNA can form very stable trinucleotide hairpin loops depending, however, strongly on the closing base pair. Replica-exchange molecular dynamics (REMD) were employed to study hairpin folding of two DNA sequences, d(gcGCAgc) and d(cgGCAcg), with the same central loop motif but different closing base pairs starting from single-stranded structures. In both cases, conformations of the most populated conformational cluster at the lowest temperature showed close agreement with available experimental structures. For the loop sequence with the less stable G:C closing base pair, an alternative loop topology accumulated as second most populated conformational state indicating a possible loop structural heterogeneity. Comparative-free energy simulations on induced loop unfolding indicated higher stability of the loop with a C:G closing base pair by ~3 kcal mol(-1) (compared to a G:C closing base pair) in very good agreement with experiment. The comparative energetic analysis of sampled unfolded, intermediate and folded conformational states identified electrostatic and packing interactions as the main contributions to the closing base pair dependence of the d(GCA) loop stability.     

Configurational entropy modulates the mechanical stability of protein GB1

Configurational entropy plays important roles in defining the thermodynamic stability as well as the folding/unfolding kinetics of proteins. Here we combine single-molecule atomic force microscopy and protein engineering techniques to directly examine the role of configurational entropy in the mechanical unfolding kinetics and mechanical stability of proteins. We used a small protein, GB1, as a model system and constructed four mutants that elongate loop 2 of GB1 by 2, 5, 24 and 46 flexible residues, respectively. These loop elongation mutants fold properly as determined by far-UV circular dichroism spectroscopy, suggesting that loop 2 is well tolerant of loop insertions without affecting GB1′s native structure. Our single-molecule atomic force microscopy results reveal that loop elongation decreases the mechanical stability of GB1 and accelerates the mechanical unfolding kinetics. These results can be explained by the loss of configurational entropy upon closing an unstructured flexible loop using classical polymer theory, highlighting the important role of loop regions in the mechanical unfolding of proteins. This study not only demonstrates a general approach to investigating the structural deformation of the loop regions in mechanical unfolding transition state, but also provides the foundation to use configurational entropy as an effective means to modulate the mechanical stability of proteins, which is of critical importance towards engineering artificial elastomeric proteins with tailored nanomechanical properties.     

The initial step of DNA hairpin folding: a kinetic analysis using fluorescence correlation spectroscopy

Conformational fluctuations of single-stranded DNA (ssDNA) oligonucleotides were studied in aqueous solution by monitoring contact-induced fluorescence quenching of the oxazine fluorophore MR121 by intrinsic guanosine residues (dG). We applied fluorescence correlation spectroscopy as well as steady-state and time-resolved fluorescence spectroscopy to analyze kinetics of DNA hairpin folding. We first characterized the reporter system by investigating bimolecular quenching interactions between MR121 and guanosine monophosphate in aqueous solution estimating rate constants, efficiency and stability for formation of quenched complexes. We then studied the kinetics of complex formation between MR121 and dG residues site-specifically incorporated in DNA hairpins. To uncover the initial steps of DNA hairpin folding we investigated complex formation in ssDNA carrying one or two complementary base pairs (dC–dG pairs) that could hybridize to form a short stem. Our data show that incorporation of a single dC–dG pair leads to non-exponential decays for opening and closing kinetics and reduces rate constants by one to two orders of magnitude. We found positive activation enthalpies independent of the number of dC–dG pairs. These results imply that the rate limiting step of DNA hairpin folding is not determined by loop dynamics, or by mismatches in the stem, but rather by interactions between stem and loop nucleotides.     

The effect of chain length on protein solubilization in polymer-based vesicles (polymersomes)

Using a mean-field analysis we derive a consistent model for the perturbation of a symmetric polymeric bilayer due to the incorporation of transmembrane proteins, as a function of the polymer molecular weight and the protein dimensions. We find that the mechanism for the inhibition of protein incorporation in polymeric bilayers differs from that of their inclusion in polymer-carrying lipid vesicles; in polymersomes, the equilibrium concentration of transmembrane proteins decreases as a function of the thickness mismatch between the protein and the bilayer core, whereas in liposomes the presence of polymer chains affects the protein adsorption kinetics. Despite the increased stiffness of polymer bilayers (when compared to lipid ones), their perturbation decay length and range of protein-protein interaction is found to be relatively long. The energetic penalty due to protein adsorption increases relatively slowly as a function of the polymer chain length due to the self-assembled nature of the polymer bilayer. As a result, we predict that transmembrane proteins may be incorporated in significant numbers even in bilayers where the thickness mismatch is large.     

Strong binding of single-stranded DNA by stem-loop oligonucleotides.

We report that oligodeoxynucleotides which form stem-loop hairpin structures and which have pyrimidine-rich loops can form strong complexes with complementary single-stranded DNA sequences. Stem-loop oligonucleotides were constructed with a 25-nt T-rich loop and with variable Watson-Crick stems. The complexes of these oligomers with the sequence dA8 were studied by thermal denaturation. Evidence is presented that the complexes are one-to-one, bimolecular complexes in which the pyrimidine loop bases comprise the outer strands in a pyr.pur.pyr triplex, in effect chelating the purine strand in the center of the loop. Melting temperatures for the loop complexes are shown to be up to 29 degrees C higher than Watson-Crick duplex of the same length. It is shown that the presence of a stem increases stability of the triplex relative to an analogous oligomer without a stem. The effect of stem length on the stability of such a complex is examined. Such hairpin oligomers represent a new approach to the sequence-specific binding of single-stranded RNA and DNA. In addition, the finding raises the possibility that such a complex may exist in natural RNA folded sequences.     

Bacterial DNA topoisomerase I can relax positively supercoiled DNA containing a single-stranded loop

Using heteroduplex molecules formed from a pair of plasmids, one of which contains a small deletion relative to the other, it is shown that bacterial topoisomerase I can relax a positively supercoiled DNA if a short single-stranded loop is placed in the DNA. This result supports the postulate that the specificity of bacterial DNA topoisomerase I for negatively supercoiled DNA in its relaxation reaction derives from the requirement of a short single-stranded DNA segment in the active enzyme-substrate complex. Nucleolytic and chemical probing of complexes between bacterial DNA topoisomerase I and heteroduplex DNA molecules containing single-stranded loops ranging from 13 to 27 nucleotides in length suggests that the enzyme binds specifically to the region containing a single-stranded loop; the site of DNA cleavage by the topoisomerase appears to lie within the single-stranded loop, with the enzyme interacting with nucleotides on both sides of the point of cleavage.     

Interaction of DNA hairpin loops and a complementary strand by a triplet of base pairs

Hypothesis of non-enzymatic recognition of primordial tRNA and mRNA precursors is experimentally approached. DNA hairpins containing a different number of deoxyguanosine residues in the loop are analyzed for their binding ability to a chemically fixed single-strand of oligo(dC). In presence of small Mg2+ concentration a hairpin with five dG residues in the loop is adsorbed to affinity matrix. Comparison of elution temperatures of hairpin oligonucleotides with those of single-stranded oligoguanylic acids with length of the loop indicates, that smallest loop able to bind forms a triplet of base pairs.     

DNA hairpins: fuel for autonomous DNA devices

We present a study of the hybridization of complementary DNA hairpin loops, with particular reference to their use as fuel for autonomous DNA devices. The rate of spontaneous hybridization between complementary hairpins can be reduced by increasing the neck length or decreasing the loop length. Hairpins with larger loops rapidly form long-lived kissed complexes. Hairpin loops may be opened by strand displacement using an opening strand that contains the same sequence as half of the neck and a "toehold" complementary to a single-stranded domain adjacent to the neck. We find loop opening via an external toehold to be 10-100 times faster than via an internal toehold. We measure rates of loop opening by opening strands that are at least 1000 times faster than the spontaneous interaction between hairpins. We discuss suitable choices for loop, neck, and toehold length for hairpin loops to be used as fuel for autonomous DNA devices.     

Nonvolatile copolymer compositions for fabricating gel element microarrays

By modifying polymer compositions and cross-linking reagents, we have developed a simple yet effective manufacturing strategy for copolymerized three-dimensional gel element arrays. A new gel-forming monomer, 2-(hydroxyethyl) methacrylamide (HEMAA), was used. HEMAA possesses low volatility and improves the stability of copolymerized gel element arrays to on-chip thermal cycling procedures relative to previously used monomers. Probe immobilization efficiency within the new polymer was 55%, equivalent to that obtained with acrylamide (AA) and methacrylamide (MA) monomers. Nonspecific binding of single-stranded targets was equivalent for all monomers. Increasing cross-linker chain length improved hybridization kinetics and end-point signal intensities relative to N,N-methylenebisacrylamide (Bis). The new copolymer formulation was successfully applied to a model orthopox array. Because HEMAA greatly simplifies gel element array manufacture, we expect it (in combination with new cross-linkers described here) to find widespread application in microarray science.     

Kinetics of internal-loop formation in polypeptide chains: a simulation study

The speed of simple diffusional motions, such as the formation of loops in the polypeptide chain, places one physical limit on the speed of protein folding. Many experimental studies have explored the kinetics of formation of end-to-end loops in polypeptide chains; however, protein folding more often requires the formation of contacts between interior points on the chain. One expects that, for loops of fixed contour length, interior loops will form more slowly than end-to-end loops, owing to the additional excluded volume associated with the "tails". We estimate the magnitude of this effect by generating ensembles of randomly coiled, freely jointed chains, and then using the theory of Szabo, Schulten, and Schulten to calculate the corresponding contact formation rates for these ensembles. Adding just a few residues, to convert an end-to-end loop to an internal loop, sharply decreases the contact rate. Surprisingly, the relative change in rate increases for a longer loop; sufficiently long tails, however, actually reverse the effect and accelerate loop formation slightly. Our results show that excluded volume effects in real, full-length polypeptides may cause the rates of loop formation during folding to depart significantly from the values derived from recent loop-formation experiments on short peptides.     

Universality in the timescales of internal loop formation in unfolded proteins and single-stranded oligonucleotides

Understanding the rate at which various parts of a molecular chain come together to facilitate the folding of a biopolymer (e.g., a protein or RNA) into its functional form remains an elusive goal. Here we use experiments, simulations, and theory to study the kinetics of internal loop closure in disordered biopolymers such as single-stranded oligonucleotides and unfolded proteins. We present theoretical arguments and computer simulation data to show that the relationship between the timescale of internal loop formation and the positions of the monomers enclosing the loop can be recast in a form of a universal master dependence. We also perform experimental measurements of the loop closure times of single-stranded oligonucleotides and show that both these and previously reported internal loop closure kinetics of unfolded proteins are well described by this theoretically predicted dependence. Finally, we propose that experimental deviations from the master dependence can then be used as a sensitive probe of dynamical and structural order in unfolded proteins and other biopolymers.     

Strong Binding of Single-stranded DNA by Stem-loop Oligonucleotides

Abstract

We report that oligodeoxynucleotides which form stem-loop hairpin structures and which have pyrimidine-rich loops can form strong complexes with complementary single-stranded DNA sequences. Stem-loop oligonucleotides were constructed with a 25-nt T-rich loop and with variable Watson-Crick stems. The complexes of these oligomers with the sequence dA_gwere studied by thermal denaturation. Evidence is presented that the complexes are one-to-one, bimolecular complexes in which the pyrimidine loop bases comprise the outer strands in a pyr · pur · pyr triplex, in effect chelating the purine strand in the center of the loop. Melting temperatures for the loop complexes are shown to be up to 29 °C higher than Watson- Crick duplex of the same length. It is shown that the presence of a stem increases stability of the triplex relative to an analogous oligomer without a stem. The effect of stem length on the stability of such a complex is examined. Such hairpin oligomers represent a new approach to the sequence-specific binding of single-stranded RNA and DNA. In addition, the finding raises the possibility that such a complex may exist in natural RNA folded sequences.     

The spatial distributions of randomly coiling polynucleotides

Statistical mechanical averages of vectors and tensors characterizing the allowed configurations of randomly coiling polynucleotides have been calculated for chains of 2⁰–2¹⁰ repeating units. Specifically, the persistence vector p = 〈 r 〉 has been obtained as a function of chain length. Configurational averages of the Cartesian tensors formed from the displacement vector ρ = r – p have been computed up to and including the tensor of seventh rank. From these tensors the three-dimensional spatial distributions of end-to-end vectors have been constructed to provide comprehensive pictures of the directional tendencies of the randomly coiling polynucleotide. The elements of the third and fourth moment tensors, however, give sufficient information to represent accurately the qualitative features of the spatial distributions. For long chains, more than 2⁶ (64) repeating units, the spatial distributions assume spherically symmetric shapes that can be adequately characterized by one-dimensional radial distribution functions. These radial distribution functions agree well with the radial distributions calculated from Monte Carlo samples containing more than 5000 chains. The constraints of fixed bond lengths, fixed bond angles, and hindered internal rotations severely distort the spatial distributions of short polynucleotide chains to mushroom-shaped volumes. These skewed distributions provide information useful to the analysis of small, single-stranded loops, bulges, and circles. The formation of these structures requires the termini of the polynucleotides to lie within specifically delineated volumes with respect to coordinate systems affixed to the first bonds of the chains. The extent to which these loop closure volumes overlap the three-dimensional spatial distributions provides estimates of loop formation that are much more reliable than earlier studies based upon the radial distribution function.     

Analysis of brush-particle interactions using self-consistent-field theory

Non-specific protein adsorption can be reduced by attaching polymer chains by one end to a sorbent surface. End-grafted polymer modified surfaces have also found application in size-based chromatographic bioseparations. To better understand how to tailor surfaces for these applications, a numerical SCF model has been used to calculate theoretical results for the polymer density distribution of interacting polymer chains around a solute particle positioned at a fixed distance from a surface. In addition, the excess energy required to move the particle into the polymer chains (interaction energy) is calculated using a statistical mechanical treatment of the lattice model. The effect of system variables such as particle size, chain length, surface density and Flory interaction parameters on density distributions and interaction energies is also studied. Calculations for the interaction of a solute particle with a surface covered by many polymer chains (a brush) show that the polymer segments will fill in behind the particle quite rapidly as it moves toward the surface. When there is no strong energetic attraction between the polymer and solute we predict that the interaction energy will be purely repulsive upon compression due to losses in conformational entropy of the polymer chains. Above a critical chain length, which depends upon particle size, a maximum in the force required to move the particle toward the surface is observed due to an engulfment of the particle as chains attempt to access the free volume behind the particle. If an attraction exists between the polymer and solute, such that a minimum in the interaction energy is seen, the optimum conditions for solute repulsion occur at the highest surface density attainable. Long chain length can lead to increased solute concentration within the polymer layer due to the fact that an increased number of favourable polymer–solute contacts are able to occur than with short chains at a similar entropic penalty.     

Effects of the transciption inhibitory protein, TF1, on phage SP01 promoter complex formation and stability.

The uptake of a homologous single-stranded fragment by superhelical DNA produces a complex that contains a stable displacement loop. When the circular DNA was relaxed by the random action of pancreatic DNAase, complexes dissociated by a process which requires that the single-stranded arm of the D-loop be intact. We attribute the dissociation to branch migration, the exchange of like strands at a branch point. The kinetics of dissociation were biphasic. A fraction of the nicked complexes dissociated in a few seconds, the rest dissociated much more slowly. The fraction of molecules that dissociated slowly was directly related to the length of the third strand, and inversely related to temperature. Salt also inhibited dissociation. Under physiological conditions, 37 °C and 0.15 m-NaCl, more than half of complexes containing a third strand of 1000-nucleotide residues survived for at least one minute. These observations provide a guide to handling certain natural or synthetic branched derivatives of DNA. Analyzing our data by the method of Thompson et al. (1976), we have estimated that the time for the exchange of one nucleotide for another at a single-stranded branch is 12 microseconds; but the calculated value depends strongly upon the assumption that single-strand branch migration occurs by a random walk.     

Length of the active-site crossover loop defines the substrate specificity of ubiquitin C-terminal hydrolases for ubiquitin chains

UCHs [Ub (ubiquitin) C-terminal hydrolases] are a family of deubiquitinating enzymes that are often thought to only remove small C-terminal peptide tails from Ub adducts. Among the four UCHs identified to date, neither UCH-L3 nor UCH-L1 can catalyse the hydrolysis of isopeptide Ub chains, but UCH-L5 can when it is present in the PA700 complex of the proteasome. In the present paper, we report that the UCH domain of UCH-L5, different from UCH-L1 and UCH-L3, by itself can process the K48-diUb (Lys48-linked di-ubiquitin) substrate by cleaving the isopeptide bond between two Ub units. The catalytic specificity of the four UCHs is dependent on the length of the active-site crossover loop. The UCH domain with a long crossover loop (usually >14 residues), such as that of UCH-L5 or BAP1 [BRCA1 (breast cancer early-onset 1)-associated protein 1], is able to cleave both small and large Ub derivatives, whereas the one with a short loop can only process small Ub derivatives. We also found that elongation of the crossover loop enables UCH-L1 to have isopeptidase activity for K48-diUb in a length-dependent manner. Thus the loop length of UCHs defines their substrate specificity for diUb chains, suggesting that the chain flexibility of the crossover loop plays an important role in determining its catalytic activity and substrate specificity for cleaving isopeptide Ub chains.     

Impurity and end effects on finite polymer chains--Ising model approach

By the use of a new trick, the open one-dimensional Ising model with nearest neighbor interactions is solved exactly to examine impurity and end effects on finite polymer chains. Melting curves are plotted for various distributions of AT and GC bonds as a function of interaction strength and chain length. Results are compared with previous calculations on infinite length chains by Montroll &; Goel. Correlation effects between impurity bonds on a finite, pure-basis chain are also studied and their implications to further studies of polymer chains indicated.     

Processivity and kinetics of the reaction of exonuclease I from Escherichia coli with polydeoxyribonucleotides

The enzyme exonuclease I from Escherichia coli hydrolyzes successive nucleotides from the 3'-termini of single-stranded deoxyribonucleotide homopolymers. When the reaction is stopped after partial hydrolysis, only intact starting material and small oligomers can be isolated. The distribution of oligomeric products varies with the base composition of the polymer but the largest oligomer that can be isolated from the reaction of exonuclease I with homopolymers of deoxyadenylate, deoxythymidylate, or deoxycytidylate is a decamer. These results suggest a model in which exonuclease I possesses at least two nucleotide binding sites. When both sites are filled, with 11-mers and longer polymers, the enzyme does not dissociate from the polymer during hydrolysis. When, with smaller oligomers, only a single site is filled, the reaction partitions at each oligomer between hydrolysis and dissociation. The kinetics of the reactions of exonuclease I with purified polydeoxyriboadenylates of defined size distributions have been investigated. The maximum rates of hydrolysis are nearly independent of polymer size while the apparent Michaelis constants are inversely proportional to the polymer size. A simple steady state model yields a kinetic equation that is consistent with our results. Competition experiments indicate that the rate at which exonuclease I associates with the 3'-terminus of a polydeoxyribonucleotide is independent of the polymer's chain length.