Effective diffusion rate through a polymer network: influence of nonspecific binding and intersegment transfer

The effective diffusion rate of a tracer molecule through a polymer network can be influenced by nonspecific binding. If such binding occurs, the local density fluctuations (segmental diffusion) of the network molecules will contribute to the net displacements of tracer molecules. If the network is strongly interconnected by entanglement or cross-linking, these local motions will only carry the tracer molecules over a small region, and effective transport would require dissociation and reassociation of the tracer molecule to another part of the network. Alternatively, tracer molecules could be transferred directly (intersegment transfer) between different parts of the network whenever they are brought sufficiently close by the density fluctuations. A wormlike-chain model for the segmental diffusion of a polymer is used to describe the network motions and to derive the effective diffusion rate for a tracer molecule as a function of network density and binding constant with or without intersegment transfer contributing. It is found that the density dependence for the effective diffusion of ethidium bromide through dense DNA solutions studied by photobleaching recovery [R. D. Icenogle and E. L. Elson (1983) Biopolymers 22 , 1949–1966] agrees with an intersegment-transfer mechanism limited by the segmental DNA motions. The calculations are also applied to a model for the intracellular diffusion of molecules loosely bound to the cytomatrix. If intersegment transfer dominates it can account for the observed size independence for the intracellular diffusion rates of various injected macromolecules.     

Association of short DNA fragments: Steady state fluorescence polarization study

We have studied aggregation/association of monodisperse DNA fragments (ranging from 30–90 base pairs) by steady-state fluorescence polarization of intercalculated ethidium. The method of excitation at different wavelengths in the ethidium absorption spectrum provides information about anisotropic twisting and tumbling mobility of the fragments. We find that end-over-end tumbling rather than axial spinning and internal twisting motions are affected by aggregation/association. The critical concentration for observing the effects of intermolecular interactions is approximately 5 mg DNA/mL at room temperature, independent of fragment length. Association is favored by low temperature and high (> 10 mM) concentration of Mg²⁺. From temperature-and salt-dependence experiments we infer that the “aggregates” are similar to those observed in a recently discovered DNA sol–gel transition [M. G. Fried and V. A. Bloomfield (1984) Biopolymers 23 , 2141–2155]. We also discuss possible arrangements of the fragments within the aggregates and their possible relation to formation of DNA liquid crystals.     

Diffusion of the Restriction Nuclease EcoRI along DNA

Many specific sequence DNA binding proteins locate their target sequence by first binding to DNA nonspecifically, then by linearly diffusing or hopping along DNA until either the protein dissociates from the DNA or it finds the recognition sequence. We have devised a method for measuring one-dimensional diffusion along DNA based on the ratio of the dissociation rate of protein from DNA fragments containing one specific binding site to the dissociation rate from DNA fragments containing two specific binding sites. Our extensive measurements of dissociation rates and specific-nonspecific relative binding constants of the restriction nuclease EcoRI enable us to determine the diffusion rate of nonspecifically bound protein along the DNA. By varying the distance between the two binding sites, we confirm a linear diffusion mechanism. The sliding rate is relatively insensitive to salt concentration and osmotic pressure, indicating that the protein moves smoothly along the DNA probably following the helical phosphate-sugar backbone of DNA. We calculate a diffusion coefficient for EcoRI of 3 × 10⁴ bp² s^− 1 EcoRI is able to diffuse ∼ 150 bp, on average, along the DNA in 1 s. This diffusion rate is about 2000-fold slower than the diffusion of free protein in solution. A factor of 40-50 can be accounted for by rotational friction resulting from following the helical path of the DNA backbone. Two possibilities could account for the remaining activation energy: salt bridges between the DNA and the protein are transiently broken, or the water structure at the protein-DNA interface is disrupted as the two surfaces move past each other.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Diffusion of DNA at very low concentrations

The diffusion behavior of DNA samples of molecular weights between 1 × 10⁶ and 25 × 10⁶ Daltons was investigated under standard conditions at mean concentrations c? between 0.0009 and 0.017 g/dl. Special techniques described previously were used and supplemented. The sensitivity required was accomplished by multiple passage through the sample cells (effective path length of 10–45 cm) and application of the Gouy interference method. The maximum DNA refraction index difference has been determined more precisely from Gouy interference fringes by applying a systematic variation procedure and a linear-plot criterion. Convection was prevented by a temperature constancy better than 0.002°C/day, vibrationless operation, and by application of a slight density gradient of heavy water, which also improved the boundary-forming procedure. The corresponding optical HDO gradient was compensated. The concentration dependence of the DNA diffusion coefficient average D_A was found to be positive and very small at extremely low concentrations, that is, below c? = 0.008 g/dl, for the sample of highest molecular weight investigated. With beginning penetration of different DNA molecules, D_A increases markedly. The diffusion constant averages of our polydisperse samples will be corrected for monodisperse subfractions in a following paper. The resulting molecular weights M from diffusion and sedimentation constants (D⁰, s⁰) together with data from literature are the basis of new s⁰–M, D⁰ ? M, and [η]–M relations for monodisperse DNA samples.     

Mode‐coupling Smoluchowski dynamics of a double‐stranded DNA oligomer

The local dynamics of a double‐stranded DNA d(TpCpGpCpG)₂ is obtained to second order in the mode‐coupling expansion of the Smoluchowski diffusion theory. The time correlation functions of bond variables are derived and the ¹³C‐nmr spin–lattice relaxation times T₁ of different ¹³C along the chains are calculated and compared to experimental data from the literature at three frequencies. The DNA is considered as a fluctuating three‐dimensional structure undergoing rotational diffusion. The fluctuations are evaluated using molecular dynamics simulations, with the ensemble averages approximated by time averages along a trajectory of length 1 ns. Any technique for sampling the configurational space can be used as an alternative. For a fluctuating three‐dimensional (3D) structure using the three first‐order vector modes of lower rates, higher order basis sets of second‐rank tensor are built to give the required mode coupling dynamics. Second‐ and even first‐order theories are found to be in close agreement with the experimental results, especially at high frequency, where the differences in T₁ for ¹³C in the base pairs, sugar, and backbone are well described. These atomistic calculations are of general application for studying, on a molecular basis, the local dynamics of fluctuating 3D structures such as double‐helix DNA fragments, proteins, and protein–DNA complexes. © 1999 John Wiley & Sons, Inc. Biopoly 50: 613–629, 1999     

The intrinsically disordered linker of E. coli SSB is critical for the release from single‐stranded DNA

The Escherichia coli single stranded DNA binding protein (SSB) is crucial for DNA replication, recombination and repair. Within each process, it has two seemingly disparate roles: it stabilizes single‐stranded DNA (ssDNA) intermediates generated during DNA processing and, forms complexes with a group of proteins known as the SSB‐interactome. Key to both roles is the C‐terminal, one‐third of the protein, in particular the intrinsically disordered linker (IDL). Previously, they have shown using a series of linker deletion mutants that the IDL links both ssDNA and target protein binding by mediating interactions with the oligosaccharide/oligonucleotide binding fold in the target. In this study, they examine the role of the linker region in SSB function in a variety of DNA metabolic processes in vitro. Using the same linker mutants, the results show that in addition to association reactions (either DNA or protein), the IDL is critical for the release of SSB from DNA. This release can be under conditions of ssDNA competition or active displacement by a DNA helicase or recombinase. Consistent with their previous work these results indicate that SSB linker mutants are defective for SSB–SSB interactions, and when the IDL is removed a terminal SSB–DNA complex results. Formation of this complex inhibits downstream processing of DNA by helicases such as RecG or PriA as well as recombination, mediated by RecA. A model, based on the evidence herein, is presented to explain how the IDL acts in SSB function.     

Theory of friction-limited DNA unwinding

The theory of friction-limited DNA unwinding is developed explicitly for moderate tind large perturbations. This extension of the earlier theory of the relaxation kinetics is necessary because of the complex nature of the rate limitation for small perturbations. The assumption of the theory that is violated under relaxation conditions is that base pairing reactions occurring at a constant local degree of twist of the strands are fast compared to the net unwinding of the molecule. However, these reactions that are slow for small perturbations have a large activation energy, and become faster than friction-limited un winding for large enough temperature jumps and sufficiently large DXA molecules. Thus only the rate for moderate and large perturbations is clearly limited by frictional resistance to turning the molecule in solution. The model used is a diffusional unwinding of the two strands, driven by the accompanying decrease in free energy. For large perturbations a numerical solution of the diffusion equation is required, since the diffusion coefficient is not constant. Two new parameters must be introduced into the equilibrium statistical theory to describe friction-limited unwinding kinetics. These are the force constant b, for winding up coil regions and the frictional coefficient per base pair β_cfor rotating coil regions in solution. We find by fitting the theory to experiment that b = 1.8 × 10^?13 ergs/ rad²- and β_c = 3.5 × 10^?21 erg see/base pair, both for DNA melted in alkali at 0.4.M Na ⁺ and ～30 °C. The latter value is in agreement with predictions based on the viscosity of single stranded DNA in alkali. The quoted value of bcan be interpreted to mean that the number of conformational states of a nucleolide is reduced by an average factor of 1.55 when it is wound around another strand to the degree of twist in a double helix, but without forming a base pair.     

Sedimentation coefficient of polyoma virus DNA

The sedimentation coefficient of the twisted circular form of polyoma virus DNA is calculated from the Kirkwood sedimentation–diffusion equation, the structure being assumed to be a rigid double superhelix. Agreement with the experimental sedimentation coefficient can be obtained, with the use of an experimental value for the number of superhelical turns, when the pitch of the superhelix is intermediate between its minimal and maximal possible values. Another model, which has been proposed for polyoma DNA at low ionic strengths, may be visualized as a superhelical structure wound about a torus. Calculations of sedimentation coefficients for this model agree qualitatively with experimental data at ionic strengths Below 10^?2M.     

The Flexibility of A-Form DNA

Abstract

We have determined the rise per base pair and persistence length of A-form DNA in trifluoroethanol solutions for fragments 350–900 base pairs in length that best describe rotational diffusion coefficients determined by transient electric birefringence. The 2.6 A spacing between base pairs found in crystal and fiber A-form structures is preserved in solution. The persistence length is about 1500 A, or about three times longer than for B-form DNA. There is no apparent electrostatic contribution to the persistence length in the salt concentration range 0.2–2.0 mM Na cacodylate. This suggests an even closer association between DNA and its neutralizing counterions than predicted by condensation theory, perhaps due to a sheath of trifluoroethanol excluded water surrounding the A-form helix.     

A critical evaluation of models for complex molecular dynamics: application of NMR studies of double- and single-stranded DNA

The nature of internal and overall motions in native (double-stranded) and denatured (single-stranded) DNA fragments 120–160 base pairs (bp) long is examined by molecular-dynamics modeling using ¹³C-nmr spin-relaxation data obtained over the frequency range of 37–125 MHz. The broad range of ¹³C frequencies is required to differentiate among various models. Relatively narrow linewidths, large nuclear Overhauser enhancements (NOEs), and short T₁ values all vary significantly with frequency and indicate the presence of rapid, restricted internal motions on the nanosecond time scale. For double-stranded DNA monomer fragments (147 bp, 24 Å diam at 32°C), the overall motion is that of an axially symmetric cylinder (τ_x = ～10^?6 s;τ_Z = ～1.8 × 10^?8s), which is in good agreement with values calculated from hydrodynamic theory (τ_x = ～1.8 × 10^?6 s; τ_Z = ～2.7 × 10^?8 s). The DNA internal motion can be modeled as restricted amplitude internal diffusion of individual C? H vectors of deoxyribose methine carbons C1′, C3′, and C4′, either with conic boundary conditions (τ_w = ～4 × 10^?9 s, θ_cone = ～21°) or as a bistable jump (τ_A = τ_B = ～2 × 10^?9 s, θ = ～15°). We discuss the critical role in molecular-dynamics modeling played by the angle (β) that individual C? H vectors make with the long axis of the DNA helix. Heat denaturation brings about increases in both the rate and amplitude of the internal motion (described by the wobble model with τ_W = ～0.2 × 10^?9 s, θ_cone = ～50°), and overall motion is affected by becoming essentially isotropic (τ_x = τ_Z = ～5 × 10^?8 s) for the single-stranded molecules. Since ¹³C-nmr data obtained at various DNA concentrations for C2′ of the deoxyribose ring is not described well by the above models, a new model incorporating an additional internal motion is proposed to take into account the rapid, extensive, and weakly coupled motion of C2′.     

Rate of intrachain contact formation in an unfolded protein: temperature and denaturant effects

We have measured the effect of temperature and denaturant concentration on the rate of intrachain diffusion in an unfolded protein. After photodissociating a ligand from the heme iron of unfolded horse cytochrome c, we use transient optical absorption spectroscopy to measure the time scale of the diffusive motions that bring the heme, located at His18, into contact with its native ligand, Met80. Measuring the rate at which this 62 residue intrachain loop forms under both folding and unfolding conditions, we find a significant effect of denaturant on the chain dynamics. The diffusion of the chain accelerates as denaturant concentration decreases, with the contact formation rate approaching a value near approximately 6x10(5) s(-1) in the absence of denaturant. This result agrees well with an extrapolation from recent loop formation measurements in short synthetic peptides. The temperature dependence of the rate of contact formation indicates an Arrhenius activation barrier, Ea approximately 20 kJ/mol, at high denaturant concentrations, comparable to what is expected from solvent viscosity effects alone. Although Ea increases by several kBT as denaturant concentration decreases, the overall rate of diffusion nevertheless increases. These results indicate that inter-residue energetic interactions do not control conformational diffusion in unfolded states, even under folding conditions.     

Dynamics and consequences of DNA looping by the FokI restriction endonuclease

Genetic events often require proteins to be activated by interacting with two DNA sites, trapping the intervening DNA in a loop. While much is known about looping equilibria, only a few studies have examined DNA-looping dynamics experimentally. The restriction enzymes that cut DNA after interacting with two recognition sites, such as FokI, can be used to exemplify looping reactions. The reaction pathway for FokI on a supercoiled DNA with two sites was dissected by fast kinetics to reveal, in turn: the initial binding of a protein monomer to each site; the protein–protein association to form the dimer, trapping the loop; the subsequent phosphodiester hydrolysis step. The DNA motion that juxtaposes the sites ought on the basis of Brownian dynamics to take ~2 ms, but loop capture by FokI took 230 ms. Hence, DNA looping by FokI is rate limited by protein association rather than DNA dynamics. The FokI endonuclease also illustrated activation by looping: it cut looped DNA 400 times faster than unlooped DNA.     

Orientational interactions in low-concentration DNA solutions

The rotational relaxation tiem τ₃ of DNA molecules (M_w ? 5 × 10⁶) in solution has been determined by the transient electric birefringence method. The analysis of the birefringence decay makes it possible to study only the higher-molecular-weight fraction, the molecules being considered as rigid elongated particles in a short time scale. A marked concentration dependence of the relaxation time has been observed for DNA in low ionic strengths. Above a critical concentration c*, τ₃ increases with the DNA concentration, c. The value of c* increases with the ionic strength. For 10^?3 ionic strength (with NaCl), c* is about 10 μg/mL; then we observe the same strong concentration dependence of rotational relaxation times as recently reported for rodlike M-13 viruses [Maguire, J. F., McTague, J. P. & Rondelez, F. (1980) Phys. Rev. Lett. 45 , 1891–1894]. These results may be discussed in terms of the Doi-Edwards theory for rotational relaxation time of rigid macromolecules [Doi, M. (1975) J. Phys. 36 , 607–611; Doi, M. & Edwards, S. F. (1978) J. Chem. Soc. Faraday Trans. 74 , 918–932] and the critical concentration above which the interactions between the molecules begin to appear allows determining the corresponding molecular length. We observe a very good agreement between the DNA lengths obtained from the c* values and by using the infinite dilution value of τ₃ and Broersma's equation. Therefore, only highly diluted solutions can be used if intrinsic molecular properties based on the rotational diffusion of high-molecular-weight elongated molecules are studied.     

Dynamics of superhelical DNA studied by photon correlation spectroscopy

We have conducted photon correlation spectroscopy (PCS) studies on the plasmid pUC8 (2717 bp) in order to elucidate the internal dynamics of this superhelical DNA. We confirm that the first-order autocorrelation function of the scattered light from pUC8 solutions can be separated into two distinct exponential decay components, as first shown by Lewis et al. (R. Lewis, J.H. Huang and P. Pecora, Macromolecules 18 (1985) 944). A thorough analysis of the dependence on scattering vector K of the rates and amplitudes of the two components enables us to assign the slowly relaxing part to the center-of-mass diffusion of the DNA, while the faster component corresponds to rotational, bending and twisting motions of the superhelix. For larger K values the internal motions can be formally expressed in terms of an 'internal diffusion coefficient' Di, whose value of 2.0-2.5 X 10(-11) m2 s-1 is approximately equal to the translational diffusion coefficient predicted for a stiff DNA piece of the persistence length, 65 nm. Comparison of our measured Di values to those predicted from a recent theory of circular worm-like coils (K. Soda, Macromolecules 17 (1984) 2365) shows that the internal motions are faster than the theoretical values. One of the reasons for this discrepancy could be that the theory does not take into account torsional motions, which contribute significantly to the internal dynamics (J.C. Thomas, S.A. Allison, C.J. Appelof and J.M. Schurr, Biophys. Chem. 12 (1980) 177). At low K values, the fast relaxation of superhelical pUC8 is no longer proportional to K2, but reaches a constant value as K approaches zero. This behavior, not seen for the linearized DNA, can be interpreted in terms of rotational diffusion of a flexible rod-like molecule (T. Maeda and S. Fujime, Macromolecules 17 (1984) 2381) and supports an interwound rod-like structure for pUC8 DNA with an average end-to-end distance of 220 nm.