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  • 1
    Electronic Resource
    Electronic Resource
    Rates of diffusion-limited reaction in periodic systems (1987)
    Springer
    Journal of statistical physics 49 (1987), S. 725-750 
    Details
    ISSN: 1572-9613
    Keywords: Pseudopotential ; perturbation theory ; boundary-value problem ; nonseparable ; Helmholtz equation ; Lambert series ; first passage time ; circles ; cylinders ; spheres ; two dimensions ; square lattice ; triangular lattice ; three dimensions ; simple cubic ; body-centered cubic ; face-centered cubic ; Sinai's billiard
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The pseudopotential and perturbation theory are used to derive the first three terms in the expansion of the smallest eigenvalue of the Helmholtz equation both for infinite two-dimensional systems with an array of perfectly absorbing circles centered on (1) a square lattice and (2) a triangular lattice, and also for infinite three-dimensional systems both with arrays of perfectly absorbing interspersed cylinders and with an array of perfectly absorbing spheres centered on (1), a simple cubic lattice, (2) a body-centered cubic lattice, and (3) a facecentered cubic lattice. In all cases, the perturbation parameter involves the ratio of the radius of the absorber to the lattice spacing. These eigenvalues and the corresponding eigenfunctions are used to compute the first three terms of expansions of the first passage time of a diffusing point particle randomly placed outside the absorbers. Expressing the perturbation parameter as a function of the area or volume fraction occupied by the absorbers reveals a remarkable similarity among the rates of diffusion-limited reaction for arrays of absorbers and the corresponding radially symmetric system containing one central absorber.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01009354
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  • 2
    Electronic Resource
    Electronic Resource
    Anomalies in sedimentation. I. Stability theory of sedimenting entanglements in the “tight-bending” limit (1973)
    New York : Wiley-Blackwell
    Biopolymers 12 (1973), S. 857-867 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A simple model is introduced to investigate the stability of a sedimenting entanglement. The sedimenting entanglement is represented by a sedimenting sieve. Solvent can pass through it, but single-chain molecules that flow into it become entangled and their flow decreases or, if permanent entanglements form, ceases entirely. With this model we are able to find the conditions under which the mass of a sedimenting entanglement remains constant, grows or decays to a stable value, grows beyond limit, or decays to the mass of a single chain. The theory is applied to the sedimentation of small concentrations of large chain molecules in solutions of small chain molecules in solutions of small chain molecules for the case in which the entanglements are long-lived. Equations are derived which, (1) give the stable entanglement mass as a function of rotor speed and concentration and, (2) for a given concentration predict the rotor speed at which the entanglement mass grows without limit. Numerical results for small concentrations of T2 DNA sedimenting in solutions of T7 DNA are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.1973.360120414
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  • 3
    Electronic Resource
    Electronic Resource
    Theory of melting of the triple helix poly (A + 2U) for a 1 : 2 mixture of Poly A to Poly U (1973)
    New York : Wiley-Blackwell
    Biopolymers 12 (1973), S. 461-475 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Zimm-Bragg theory is extended to treat the melting of the triple helix poly (A + 2U) for a solution with a 1 : 2 mole ratio of poly A to poly U. Only the case for long chains is considered. For a given set of parameters the theory predicts the fraction of segments in the triple helix, double helix, and random coil states as a function of temperature.Four nucleation parameters are introduced to describe the two order-disorder transitions (poly (A + 2U) ⇄ poly A + 2 poly U and poly (A + U) ⇄ poly A + poly U) and the single order-order transition (poly (A + 2U) ⇄ poly (A + U) + poly U). A relation between the nucleation parameters is obtained which reduces the number of independent parameters to three. A method for determining these parameters from experiment is presented. From the previously published data of Blake, Massoulié and Fresco8 for [Na+] = 0.04, we find σT = 6.0 × 10-4, σD = 1.0 × 10-3, and σσ* = 1.5 × 10-3. σT and σD are the nucleation parameters for nucleating a triple helix and double helix, respectively, from a random coil region. σσ* is the nucleation parameter for nucleating a triple helix from a double helix and a single strand.Melting curves are generated from the theory and compared with the experimental melting curves.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.1973.360120302
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  • 4
    Electronic Resource
    Electronic Resource
    Equilibrium theory for the binding of bivalent antibodies to regularly spaced sites on a DNA moleculeThis work was supported by the National Institutes of Health Grant GM35556 and by the United States Department of Energy. (1987)
    New York : Wiley-Blackwell
    Biopolymers 26 (1987), S. 297-314 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In the autoimmune disease, Systemic Lupus Erythematosus, an individual produces antibodies that bind to his or her own DNA. In this paper we consider a single, long DNA-like molecule in a solution containing bivalent antibodies that can bind to the DNA molecule at regularly spaced sites. The antibody can be attached to DNA by either one or two binding sites. We assume that, when an antibody molecule binds through both its sites, it spans a fixed number of free sites that remain accessible to antibody binding. In this model, antibody molecules can interdigitate along the DNA molecule. We allow steric hindrance within such interdigitating clusters of bound antibodies. We derive analytical expressions for the average number of free, monovalently bound and bivalently bound antibodies, and see how this distribution is influenced by steric hindrance and by the relative binding strengths of the singly and doubly bound antibody.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360260210
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