Abstract: The depletion theory of nanoparticles immersed in a semidilute polymer solution is reinterpreted in terms of depleted chains of polymer segments. Limitations and extensions of mean-field and scaling theories are discussed. An explicit expression for the interaction between two small spheres is also reviewed. The depletion free energy for a particle of general shape is given in terms of the capacitance or effective Stokes radius. This affords a reasonable explanation for the effect of polymer on protein precipitation.
Abstract: A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits. It is argued that there are several regimes in between the de Gennes and Odijk limits introduced long ago. The DNA chain folds back on itself giving rise to a global persistence length that may be very large owing to entropic deflection. Moreover, there is an orientational excluded-volume effect between the DNA segments imposed solely by the nanoconfinement. These two effects cause the chain statistics to be intricate leading to nontrivial power laws for the chain extension in the intermediate regimes. It is stressed that DNA confinement within nanochannels differs from that in nanoslits because the respective orientational excluded-volume effects are not the same.
Abstract: Molecular confinement offers new routes for arraying large DNA molecules, enabling single-molecule schemes aimed at the acquisition of sequence information. Such schemes can rapidly advance to become platforms capable of genome analysis if elements of a nascent system can be integrated at an early stage of development. Integrated strategies are needed for surmounting the stringent experimental requirements of nanoscale devices regarding fabrication, sample loading, biochemical labeling, and detection. We demonstrate that disposable devices featuring both micro- and nanoscale features can greatly elongate DNA molecules when buffer conditions are controlled to alter DNA stiffness. Furthermore, we present analytical calculations that describe this elongation. We also developed a complementary enzymatic labeling scheme that tags specific sequences on elongated molecules within described nanoslit devices that are imaged via fluorescence resonance energy transfer. Collectively, these developments enable scaleable molecular confinement approaches for genome analysis.
Abstract: A theory is presented for lambda(C), the coefficient of the first-order correction in the density of the collective diffusion coefficient, for protein spheres interacting by electrostatic and adhesive forces. An extensive numerical analysis of the Stokesian hydrodynamics of two moving spheres is given so as to gauge the precise impact of lubrication forces. An effective stickiness is introduced and a simple formula for lambda(C) in terms of this variable is put forward. A precise though more elaborate approximation for lambda(C) is also developed. These and numerically exact expressions for lambda(C) are compared with experimental data on lysozyme at pH 4.5 and a range of ionic strengths between 0.05M and 2M. (c) 2007 American Institute of Physics.
Abstract: We investigate theoretically the fluid-crystal coexistence of solutions of globular charged nanoparticles such as proteins and inorganic colloids. The thermodynamic properties of the fluid phase are computed via the optimized Baxter model P. Prinsen and T. Odijk [J. Chem. Phys. 121, 6525 (2004)]. This is done specifically for lysozyme and silicotungstates for which the bare adhesion parameters are evaluated via the experimental second virial coefficients. The electrostatic free energy of the crystal is approximated by supposing the cavities in the interstitial phase between the particles are spherical in form. In the salt-free case a Poisson-Boltzmann equation is solved to calculate the effective charge on a particle and a Donnan approximation is used to derive the chemical potential and osmotic pressure in the presence of salt. The coexistence data of lysozyme and silicotungstates are analyzed within this scheme, especially with regard to the ionic-strength dependence of the chemical potentials. The latter agree within the two phases provided some upward adjustment of the effective charge is allowed for. (c) 2006 American Institute of Physics.
Abstract: We perform Monte Carlo simulations on the hard-core attractive Yukawa system to test the optimized Baxter model that was introduced by Prinsen and Odijk [J. Chem. Phys. 121, 6525 (2004)] to study a fluid phase of spherical particles interacting through a short-range pair potential. We compare the chemical potentials and pressures from the simulations with analytical predictions from the optimized Baxter model. We show that the model is accurate to within 10% over a range of volume fractions from 0.1 to 0.4, interaction strengths up to three times the thermal energy, and interaction ranges from 6% to 20% of the particle diameter, and performs even better in most cases. We furthermore establish the consistency of the model by showing that the thermodynamic properties of the Yukawa fluid computed via simulations may be understood on the basis of one similarity variable, the stickiness parameter defined within the optimized Baxter model. Finally, we show that the optimized Baxter model works significantly better than an often used, naive method determining the stickiness parameter by equating the respective second virial coefficients based on the attractive Yukawa and Baxter potentials. (c) 2006 American Institute of Physics.
Abstract: A theory is presented of the elongation of double-stranded DNA confined in a nanochannel based on a study of the formation of hairpins. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The DNA in the hairpin remains double-stranded. The free energy of the hairpin is significantly larger than what one would expect if this entropic effect were unimportant. As a result, the distance between hairpins or the global persistence length is often tens of micrometer long and may even reach millimeter sizes for 10 nm thin channels. The hairpin shape and size and the DNA elongation are computed for nanoslits and circular and square nanochannels. A comparison with experiment is given. (c) 2006 American Institute of Physics.
Abstract: To study the dynamics and organization of the DNA within isolated Escherichia coli nucleoids, we track the movement of a specific DNA region. Labeling of such a region is achieved using the Lac-O/Lac-I system. The Lac repressor-GFP fusion protein binds to the DNA section where tandem repeats of the Lac operator are inserted, which allows us to monitor the motion of the DNA. The movement of such a GFP spot is followed at 48 ms temporal resolution during 12 s. The spots are found to diffuse within a confined space, so that the nucleoid appears to behave like a viscoelastic network. The distribution of the &DPRIME; particle&DPRIME; position in time can be fitted to a Gaussian function indicating that the motion of the particle is Brownian. Ail average self-diffusion constant D-s = 0.12 μ m(2) s(-1) is derived via the time auto-correlation functions of the displacement and is compatible with the collective diffusion coefficient measured previously by dynamic light scattering. Restriction of a DNA sequence to a small region of the nucleoid is tentatively related to the existence of so-called supercoiling domains. © 2005 Elsevier Inc. All rights reserved.
Abstract: The dynamics of water and sodium counter-ions (Na+) in a C222(1) orthorhombic beta-lactoglobulin crystal is investigated by means of 5 ns molecular dynamics simulations. The effect of the fluctuation of the protein atoms on the motion of water and sodium ions is studied by comparing simulations in a rigid and in a flexible lattice. The electrostatic interactions of sodium ions with the positively charged LYS residues inside the crystal channels significantly influence the ionic motion. According to our results, water molecules close to the protein surface undergo an anomalous diffusive motion. On the other hand, the motion of water molecules further away from the protein surface is normal diffusive. Protein fluctuations affect the diffusion constant of water, which increases from 0.646 +/- 0.108 to 0.887 +/- 0.41 nm(2) ns(-1), when protein fluctuations are taken into account. The pore size (0.63-1.05 nm) and the water diffusivities are in good agreement with previous experimental results. The dynamics of sodium ions is disordered. LYS residues inside the pore are the main obstacles to the motion of sodium ions. However, the simulation time is still too short for providing a precise description of anomalous diffusion of sodium ions. The results are not only of interest for studying ion and water transport through biological nanopores, but may also elucidate water-protein and ion-protein interactions in protein crystals.
Abstract: DNA regions close to the origin of replication were visualized by the green fluorescent protein (GFP)-Lac repressor/lac operator system. The number of oriC-GFP fluorescent spots per cell and per nucleoid in batch-cultured cells corresponded to the theoretical DNA replication pattern. A similar pattern was observed in cells growing on microscope slides used for time-lapse experiments. The trajectories of 124 oriC-GFP spots were monitored by time-lapse microscopy of 31 cells at time intervals of 1, 2, and 3 min. Spot positions were determined along the short and long axis of cells. The lengthwise movement of spots was corrected for cell elongation. The step sizes of the spots showed a Gaussian distribution with a standard deviation of similar to 110 nm. Plots of the mean square displacement versus time indicated a free diffusion regime for spot movement along the long axis of the cell, with a diffusion coefficient of 4.3 +/- 2.6 x 10(-5) mu m(2)/s. Spot movement along the short axis showed confinement in a region of the diameter of the nucleoid (similar to 800 nm) with an effective diffusion coefficient of 2.9 +/- 1.7 x 10(-5) mu m(2)/s. Confidence levels for the mean square displacement analysis were obtained from numerical simulations. We conclude from the analysis that within the experimental accuracy - the limits of which are indicated and discussed - there is no evidence that spot segregation requires any other mechanism than that of cell (length) growth. (C) 2005 Elsevier Inc. All rights reserved.
Abstract: Several controversial issues concerning the packing of linear DNA in bacteriophages and globules are discussed. Exact relations for the osmotic pressure, capsid pressure and loading force are derived in terms of the hole size inside phages under the assumption that the DNA globule has a uniform density. A new electrostatic model is introduced for computing the osmotic pressure of rod-like polyelectrolytes at very high concentrations. At intermediate packing, a reptation model is considered for DNA diffusing within a toroidal globule. Under tight-packing conditions a model of Coulomb sliding friction is proposed. A general discussion is given of our current understanding of the statics and dynamics of confined DNA in the context of the following experiments: characterization of the liquid crystalline phases, X-ray scattering by phages, osmotic-stress measurements, cyclization within globules and single-molecule determination of the loading forces.
Abstract: A theory of nonlinear convective depletion is set up as a nanosphere translates fast through a semidilute polymer solution. For nanospheres a self-consistent field theory in the Rouse approximation is often legitimate. A self-similar solution of the convective depletion equation is argued to be feasible at high velocities. The nature of the thin boundary layer in front of the propagating particle is analyzed. One example of convective depletion is when a charged protein moves through a semidilute polymer under the influence of a high electric field. The protein velocity is then proportional to the fifth power of the field. The theory could be useful in interpreting the separation of protein mixtures by microchip electrophoresis. (C) 2004 Elsevier B.V. All rights reserved.
Abstract: A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction. (C) 2004 American Institute of Physics.
Abstract: The curvature stress of DNA packed inside a phage is balanced against its electrostatic self-interaction. The DNA density is supposed nonuniform and as a result the Donnan effect is also inhomogeneous. The coarse-grained DNA density is a nonlinear function of the DNA radius of curvature at a given position inside the bacteriophage. It turns out that a region (or regions) exists totally free from DNA. The size of such holes is computed.
Abstract: The sedimentation of DNA supercoils and bacterial nucleoids is discussed in terms of an asymptotic expression for the size of branched supercoils exhibiting an excluded-volume effect between superhelical segments. A Kirkwood-Riseman approximation is adopted for the sedimentation coefficient. The theory predicts the sedimentation of DNA supercoils fairly well despite their relatively small size in current simulations and experiments. We introduce a crosslinked supercoil model for bacterial nucleoids that are known to contain a variety of adsorbed proteins. Sedimentation experiments of the 1970s are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.
Abstract: Drag reduction is investigated in one- and two-dimensional turbulent flows that are stationary and homogeneous. In the two-dimensional case, the polymer chains are deformed though advected passively through the Kraichnan cascades within a scaling analysis. The typical rate of shear must then be larger than the time of deformation of a chain. Ultimately, elastic forces compete with Reynolds stresses at an elastic cut-off similar to that defined in the Tabor-de Gennes scenario in three dimensions. There are several regimes in two dimensions because there are two cascades. In the one-dimensional case, a Burgers-type equation is coupled to a frame-indifferent equation for the viscoelastic Maxwell stress together with a stochastic force. Dissipation arises within viscoelastic shocks. The (effectively longitudinal) speed of the elastic waves is a cut-off for the shocks. This elastic cut-off shows up in velocity correlations. The implications for soap film and wire experiments are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.
Abstract: The Doi-Shimada-Okano [J. Chem. Phys. 88, 4070 (1988)] theory of the spinodal decomposition in a suspension of rods is reinvestigated analytically. Short enough rods may rotate fairly unhindered so we emphasize translational diffusion. The excluded-volume effect between the rods gives rise to a coupling of the orientational and translational degrees of freedom. This effect may be addressed correctly because the kernel in the equation describing the dynamic evolution of the one-particle distribution turns out to be degenerate. The two principal eigenvalues calculated analytically agree with previous numerical work by Maeda [Macromolecules 22, 1881 (1989); 23, 1464 (1990)]. It is concluded that the associated relaxation modes do not represent pure density and orientation fluctuation modes.
Abstract: Numerous protocols for the isolation of bacterial nucleoids have been described based on treatment of cells with sucrose-lysozyme-EDTA and subsequent lysis with detergents in the presence of counterions (e.g., NaCl, spermidine). Depending on the lysis conditions both envelope-free and envelope-bound nucleoids could be obtained, often in the same lysate. To investigate the mechanism(s) involved in compacting bacterial DNA in the living cell, we wished to isolate intact nucleoids in the absence of detergents and high concentrations of counterions. Here, we compare the general lysis method using detergents with a procedure involving osmotic shock of Escherichia coil spheroplasts that resulted in nucleoids free of envelope fragments. After staining the DNA with DAPI (4',6-diamidino-2-phenylindole) and cell lysis by either isolation procedure: free-floating nucleoids could be readily visualized in fluorescence microscope preparations. The detergent-salt and the osmotic-shock nucleoids appeared as relatively compact structures under the applied ionic conditions of 1 M and 10 mM, respectively. RNase treatment caused no dramatic changes in the size of either nucleoid. (C) 2001 Societe francaise de biochimie et biologie moleculaire / Editions scientifiques et medicales Elsevier SAS
Abstract: Nucleoids of Escherichia coli were isolated by osmotic shock under conditions of low salt in the absence of added polyamines or Mg2+. As determined by fluorescence microscopy, the isolated nucleoids in 0.2 M NaCl are expanded structures with an estimated volume of about 27 mum(3) according to a procedure based on a 50% threshold for the fluorescence intensity. The nucleoid volume is measured as a function of the concentration of added polyethylene glycol. The collapse is a continuous process, so that a coil-globule transition is not witnessed. The Helmholtz free energy of the nucleoids is determined via the depletion interaction between the DNA helix and the polyethylene glycol chains. The resulting compaction relation is discussed in terms of the current theory of branched DNA supercoils and it is concluded that the in vitro nucleoid is crosslinked in a physical sense. Despite the congested and crosslinked state of the nucleoid, the relaxation rate of its superhelical segments, as monitored by dynamic light scattering, turns out to be purely diffusional. At small scales, the nucleoid behaves as a fluid. (C) 2001 Elsevier Science (USA).
Abstract: We explore the separation of aqueous protein - polysaccharide solutions into two liquid phases. In particular, we have studied the combinations beta-lactoglobulin/pullulan, alpha-lactalbumin/pullulan, and other examples from the literature under a variety of conditions such as varying salt content, pH (in most cases at the isoelectric point), and protein radius. We restrict ourselves to relatively small proteins (globular) and long polysaccharide chains, The mechanism behind the phase separation is explained in terms of the depiction interaction (i.e., the cross-interaction) in a suspension of small spheres (proteins) immersed in a semidilute solution of coils (polysaccharide) forming an entangled network. Weak, attractions between the spheres have been taken into account by assuming the formation of small clusters. As a general rule, we Find that the depletion free energy per protein particle governing the protein partitioning in the phase equilibrium is linear in the polysaccharide concentration over the whole range of experimentally accessible coexistence curves. Furthermore, the proportionality constant is shown to be a very useful quantity to understand the characteristics of the coexistence curves. The linearity thus found is supported by theoretical arguments developed by de Gennes and Odijk.
Abstract: The depletion interaction between nanoparticles and flexible polymers is discussed when the suspensions are nondilute. It is argued that a mean-field approximation is often useful. It is shown that the capacitance is a variable of interest for a nanoparticle immersed in a semidilute polymer solution. We also investigate the contraction of a polymer chain in a fixed array of nanosized obstacles. The contraction of a chain in a semidilute suspension of proteins is viewed as a problem of osmotic equilibrium. (C) 2000 Elsevier Science B.V. All rights reserved.
Abstract: A semiquantitative theoretical discussion is given of a DNA nucleoid escaping from a bacterial cell after lysis. There is a strong excluded-volume effect causing the nucleoid to expand, though it may be held together globally by various constraints. Tt is argued that the friction is dominated by the fairly local motion of superhelical segments. In an intermediate regime, hydrodynamic screening is strong. Tn a diffusion model a self-similar solution is presented of the non-linear diffusion equation. An affinely deforming model for the expanding nucleoid is also given. The predicted rate of expansion seems to be in qualitative accord with recent, preliminary experiments on lysed Escherichia coli viewed under the microscope. (C) 2000 Elsevier Science B.V. All rights reserved.
Abstract: We consider the effect of polymer depletion on the transport (diffusion and electrophoresis) of small proteins through semi-dilute solutions of a flexible polymer. A self-consistent field theory may be set up in the important case of quasi-ideal interactions when the protein is small enough. Dynamic depletion, the reorganization of the depletion layer as the protein diffuses, is computed within a free-draining approximation. The transport of the dressed particle (protein + depletion layer) is tackled by extending Ogston's analysis of probe diffusion through fibrous networks to the case of a probe diffusing through a semi-dilute polymer inhomogeneous on the scale of the polymer correlation length. The resulting exponential retardation agrees almost quantitatively with that found in recent electrophoresis experiments of small proteins in polymer solutions that have been ascertained to be semi-dilute (S. P. Radko and A. Chrambach, Electrophoresis, 17:1094-1102, 1996; Biopolymers, 4:183-189, 1997).
Abstract: We present an analytical calculation of the electrostatic interaction in a pletonemic supercoil within the Poisson-Boltzmann approximation. Undulations of the supercoil strands arising from thermal motion couple nonlinearly with the electrostatic interaction, giving rise to a strong enhancement of the bare interaction. In the limit of fairly tight winding, the free energy of a plectonemic supercoil may be split into an elastic contribution containing the bending and torsional energies and an electrostatic-undulatory free energy. The total free energy of the supercoil is minimized according to an iterative scheme, which utilizes the special symmetry inherent in the usual elastic free energy of the plectoneme. The superhelical radius, opening angle, and undulation amplitudes in the radius and pitch are obtained as a function of the specific linking difference and the concentration of monovalent salt. Our results compare favorably with the experimental values for these parameters of Boles et al. (1990. J. Mol. Biol. 213:931-951). In particular, we confirm the experimental observation that the writhe is a virtually constant fraction of the excess linking number over a wide range of superhelical densities. Another important prediction is the ionic strength dependence of the plectonemic parameters, which is in reasonable agreement with the results from computer simulations.
Abstract: A tentative theory is presented of microfibrillar buckling within compressed fibers. A quantitative harmonic analysis is given of the semiclassical buckling of a clamped stiff chain; the influence of thermal undulations is incorporated in Euler buckling. A scaling analysis including entropy allows one to understand semiclassical buckling. The buckling of a microfibril within a fibrous environment is analyzed in two limits: (a) when the fiber is incompressible; (b) when the matrix is assumed to be a fixed harmonic potential. In the latter case, a network of microfibrils may melt at high enough compression before the usual bucking occurs. We also study the renormalization of the confining potential by long-range elastic fields. A provisional comparison with experimental studies on macroscopic failure is given. (C) 1998 American Institute of Physics.
Abstract: A dimensional relation between the superhelical pitch angle and the superhelical radius is derived for plectonemic DNA. A uniform classical Hamiltonian is extracted from the free energy of the supercoil. The DNA superhelix may be perturbed by a variety of sources, but this does not alter the theoretical argumentation. Semiclassical arguments are presented for the validity of the analysis although one may simply appeal to establishing a classical superhelical "trajectory" experimentally. The theory is in good agreement with the microscopic determination of the plectonemic dimensions of closed circular DNA by T.C. Boles et al. (J. Mol. Biol. 213 (1990) 931). (C) 1998 Elsevier Science B.V. All rights reserved.
Abstract: The statistical mechanics of the steady state of a decaying two-dimensional turbulent liquid is extended to the case when the fluid is polymeric. The simple liquid in the rheological fluid is replaced by a vortex gas in a description of the free energy at negative temperatures. The resulting equation of motion must coincide with the inviscid limit of the rheological equation of motion. This gives an expression for the polymeric free energy in terms of the normal stresses. An axisymmetric coherent vortex is discussed and the highly nonlinear equation of motion is addressed qualitatively. The influence of the polymer is to broaden the coherent vortex. (C) 1998 Elsevier Science B.V. All rights reserved.
Abstract: A theory is presented of the phase separation of supercoiled DNA into a nucleoid in a bacterial cell. The suspension consists of DNA interacting with globular proteins in excess salt. A cross virial between DNA and a protein is computed as well as the DNA self-energy arising from excluded volume. The cellular parameters of Escherichia coli would appear to be compatible with the thermodynamic equilibrium derived theoretically. The state of superhelical DNA in the nucleoid could be liquid crystalline and rippled. (C) 1998 Elsevier Science B.V. All rights reserved.
Abstract: A continuum computation is proposed for the bending stress stabilizing DNA that is hexagonally packed within bacteriophage T7. Because the inner radius of the DNA spool is rather small, the stress of the curved DNA genome is strong enough to balance its electrostatic self-repulsion so as to form a stable hexagonal phase. The theory is in accord with the microscopically determined structure of bacteriophage T7 filled with DNA within the experimental margin of error.
Abstract: The polymer segment distribution is shown to obey the Laplace equation for a suspension of small protein spheres and semidilute polymer. The depletion interaction is computed at all protein concentrations by introducing void distributions. Within a linear response Ansatz for the solution to the Laplace equation, the average depletion energy depends on two- and three-point void (-surface) correlation functions. It is concluded that depletion correlations of long range do not appear at high protein concentrations. (C) 1997 American Institute of Physics.
Abstract: A qualitative rule is formulated for the shape deformation of DNA condensates, in which the surface stresses are balanced against bending forces. A quantitative analysis is presented for toroidal globules. Low surface tensions lead to ideal tori, high tensions give rise to compact toroids with thin inner tubes. A qualitative discussion is given of Laemmli's experiments on globules of monomolecular DNA.
Abstract: The entropy of tightly bent DNA is investigated in a variety of problems: closure probabilities, hairpin formation, nicked coils, plectonemic supercoiling, all in states with liquid-crystalline order. A new semiclassical method is presented for deriving the Green function of a tightly curved wormlike chain. Precise estimates for the entropy arising from undulations are given for tightly bent DNA in weak, intermediate, and strong nematic fields. A formal statistical mechanical analysis is outlined for hairpins and supercoils. The elongation of closed DNA without twist is computed in strong nematic fields. A scaling theory is given for a liquid crystal of untwisted DNA rings in which nematic order and ring elongation are self-consistently coupled. The elongation of plectonemic supercoils is evaluated for weak and strong nematic fields. The pitch of a cholesteric phase of plectonemic or loose supercoils is shown to be directly related to their writhe. (C) 1996 American Institute of Physics.
Abstract: How do orientational order and configurational entropy couple with micellar growth and intermicellar forces in liquid-crystalline phases? Rather severe approximations have to be employed in this formidably difficult problem in statistical mechanics. Recent progress in the field of ordered phases of elongated micelles centers on the necessity of including the undulatory entropy to circumvent potentially explosive growth in nematic and hexagonal phases. A quantitative understanding of experimental phase transitions is definitely lacking.
Abstract: We propose a theory for the zero-shear viscosity of a dilute solution of wormlike micelles, with a length distribution as derived by Israelachvili, Mitchell, and Ninham. An analytical approach using Bohdanecky's approximation to the full Yamakawa-Fujii-Yoshizaki description (YFY) for the viscosity of wormlike objects is combined with a numerical integration of the YFY equations. In principle, this provides a convenient means of extracting the growth parameters, dimensions, and persistence length of linear micelles from measurements of the viscosity as a function of the surfactant concentration.
Abstract: A model is proposed for polymer- and salt-induced toroidal condensates of DNA, based on a recent theory of the undulation enhancement of the electrostatic interaction in the bulk hexagonal phase of semiflexible polyions. In a continuum approximation, the thermodynamic potential of a monomolecular toroid may be split up in bulk, surface, and curvature contributions. With the help of an approximate analytical minimization procedure, the optimal torus dimensions are calculated as a function of the concentrations of inert polymer and added salt. The stability of the torus is analyzed in terms of its surface tension and a bulk melting criterion. The theory should be applicable to psi-toroids that are not too thick.
Abstract: We study semidilute and concentrated solutions of mononucleosomal DNA at three different NaCl concentrations by static and dynamic light scattering, viscosity, and electron cryomicroscopy. At low enough DNA concentrations the second virial coefficient behaves in the usual manner and can be interpreted by a charged rod model. It is possible to understand the concentration and scattering vector dependence of the scattering with the help of recent theoretical analyses of semidilute solutions of charged rods. Moreover, the mutual friction coefficient is in accord with the theory of hydrodynamic screening. At a certain critical concentration which increases with added salt, the intensity of the equilibrium static scattering increases several 100-fold, indicating the DNA aggregates. The dynamic scattering is in line with the static scattering; a very long decay time seems to be associated with the DNA aggregates. Freeze electron micrographs definitely bear out the existence of DNA globules which appear to form loose aggregates. Precautions have been taken to ensure there are no spurious contaminants to the best of our knowledge. Long-range attractive forces between polyions have been postulated recently within the framework of a semiquantitative theory; these ideas are tested by analyzing the ionic-strength dependence of the third virial coefficient and the onset of aggregation.
Abstract: A theoretical analysis is given of undulation-enhanced forces in solutions of semiflexible polyelectrolytes. Undulation enhancement is fairly weak when the system is isotropic, nematic or cholesteric. Electrostatic repulsion can easily be enhanced by an order of magnitude in hexagonal gels. Van der Waals forces are perturbed mildly by configurational fluctuations although their enhancement does affect the free energy function near the secondary minimum. A stability analysis of enhanced electrostatic versus Van der Waals forces is presented in order to discuss experiments on gels of tobacco mosaic virus.
Abstract: The recently discovered attractive force between hydrophobic surfaces is incorporated in a theory of polyelectrolyte solutions. Its influence on the second and third virial coefficients is estimated. Binary collisions between two polyions are virtually unaffected by attractive forces of long range whereas the impact on the third virial coefficient is enormous. The theoretical coefficients are compatible with those determined for solutions of rodlike xanthan by Kawakami and Norisuye. When the third virial coefficient is negative, the solution may become unstable. This instability appears to explain the onset of aggregation of DNA. The long-range attraction is strong enough to enforce stability of a hexagonal phase at low ionic strength. The predicted spacings agree with those found for tobacco mosaic virus by Millman et al.
Abstract: We formulate an equation for the dynamic sedimentation of linear micelles (both rodlike and flexible) in the limit of local thermodynamic equilibrium when the recombination and scission of micelles are fast processes. A self-similar solution of the first kind is proposed for rodlike micelles in a free-draining approximation. The analytical structure of the associated nonlinear ordinary differential equation is very different from that pertaining to solutions of nonaggregating molecules. The theory may be of use in an experimental determination of the growth parameters by ultracentrifugation.
Abstract: A self-consistent theory is developed for the hexagonal phase of semiflexible polyelectrolytes. The electrostatic interactions analyzed in the Poisson-Bolzmann approximation, couple non-linearly to the undulations of the polyions so that the intermolecular forces may be enhanced by an order of magnitude. The theory is in good agreement with the osmotic stress measurements on DNA by Podgornik et al. It also seems to bear on unresolved discrepancies arising in stress experiments on tobacco mosaic virus and muscle thin filament.
Abstract: A deflection length determines the statistical physics of a tightly bent wormlike chain because the undulations of the chain must follow its 'classical'' path. The deflection length which is proportional to the square of the radius of the classical path and inversely proportional to the persistence length, is interpreted to be a critical scale,. By comparing it to the usual deflection length for a wormlike chain confined by various forces, we can distinguish regimes of weak and strong bending. A scaling analysis is given of various problems: DNA packed in tori and phages, worms wound around cylinders, adsorption on spheres, hairpin and disclination defects in polymer nematics.
Abstract: A melting criterion for charged semi-flexible systems is formulated by combining the Lindemann rule with the theory of undulation-enhanced interactions. The predicted Lindemann ratios are constant along the melting curves for the lamellar phase of didodecyldimethylammonium bromide and the hexagonal phase of DNA. For connected systems there appears to be an unexplained spread in the Lindemann ratios.
Abstract: We introduce a dynamic scaling hypothesis which connects the self-diffusion of a chain with the viscosity of the macromolecular solution. It applies to both semidilute and concentrated solutions and leaves the detailed motion of the chains unspecified. When it is valid, one is able to measure the density nu of effective dynamic units in the transient network of entangled chains. The feasibility of the hypothesis is shown for aqueous poly(ethylene oxide) and sodium poly(styrenesulfonate), polymers not at all conforming to the usual scaling dynamics. Surprisingly, the density nu is not very sensitive to charge or the addition of salt.
Abstract: Scaling theory hypothesizes a step-function profile for the segment density of polymer chains terminally attached to a planar wall. Using a self-consistent-field theory we give a perturbation analysis of the first-order correction to the step-function profile in order to gauge the impact of a possible tail. The new profile decays smoothly to zero without a discontinuity in the derivative (except near the wall). The segment density profile as scaled by the amplitude of the step-function profile has a tail that decays essentially as 1/beta-z*2, with beta a dimensionless parameter and z* the distance from the wall scaled by the step length of the step-function profile. A scaling analysis would yield z*-4/3.
Abstract: The second and third virial coefficients are estimated for a semidilute suspension of macromolecular rods interacting by van der Waals forces. Whenever the attractive interaction becomes strong enough to be noticeable, it is no longer quantitatively correct to adopt a second virial approximation. Nevertheless, the statistical properties of the second virial fluid are investigated because it is a very convenient idealization of strongly interacting molecular fluids. Sufficient conditions for the local thermodynamic stability of the isotropic phase are set up. The coupling of orientational with translational degrees of freedom which arises from the anisotropic van der Waals interaction between two rods is particularly manifest in the structure factor. This is calculated analytically with the help of a variational theorem.
Abstract: We have studied dilute and semidilute solutions of poly(gamma-benzyl-L-glutamate) in 1,2-dichloroethane by static and dynamic light scattering. The aggregational behaviour of the semiflexible polymer is evidenced in both static and dynamic scattering, and is sensitive to the temperature and the polypeptide molecular weight. In particular, both the reciprocal specific scattering intensity and the effective decay rate of the dynamic correlations exhibit a minimum as a function of the concentration. The slope of effective diffusion coefficient versus the square of the scattering vector displays an anomalous maximum as a function of the concentration which can also be attributed to aggregation. The experimental evidence is compatible with head-to-tail dimerization of the polymer as the concentration increases.
Abstract: At low ionic strength counterions cluster nonuniformly around a linear, highly charged micelle. The micelle is regarded as a finite line charge with relatively fewer counterions condensing on the two ends. The end contribution to the electrostatic free energy is positive, so that the micelles shorten upon addition of simple salt to the solution.
Abstract: Polyelectrolytes may bind to oppositely charged micelles to form soluble complexes. The onset of complexation is known to obey an empirical rule connecting the surface charge densities of the polyion and the micelle with the ionic strength. We argue that this restricts severely the types of viable statistical theories of complexation. A scaling analysis rationalizes the empirical law and shows which dimensionless groups are unimportant at the onset of complexation.
Abstract: The electrostatics of micellar growth is reviewed and extended for solutions containing excess salt. In dilute solution the expansion of a linear micelle with increasing salt concentration is explained for a wide range of ionic strength. When the micellar charge density is very high, counterions condense nonuniformly onto the micellar rod. In that case the micelle may contract upon the addition of salt. In semidilute solutions the excluded-volume effect is an additional factor complicating the ionic strength dependence of micellar growth.
