On the application of geometric probability theory to polymer networks and suspensions, I

The concentration of biomarkers, such as DNA, prior to a subsequent detection step may facilitate the early detection of cancer, which could significantly increase chances for survival. In this study, the partitioning behavior of mammalian genomic DNA fragments in a two-phase aqueous micellar system was investigated using both experiment and theory. The micellar system was generated using the nonionic surfactant Triton X-114 and phosphate-buffered saline (PBS). Partition coefficients were measured under a variety of conditions and compared with our theoretical predictions. With this comparison, we demonstrated that the partitioning behavior of DNA fragments in this system is primarily driven by repulsive, steric, excluded-volume interactions that operate between the micelles and the DNA fragments, but is limited by the entrainment of micelle-poor, DNA-rich domains in the macroscopic micelle-rich phase. Furthermore, the volume ratio, that is, the volume of the top, micelle-poor phase divided by that of the bottom, micelle-rich phase, was manipulated to concentrate DNA fragments in the top phase. Specifically, by decreasing the volume ratio from 1 to 1/10, we demonstrated proof-of-principle that the concentration of DNA fragments in the top phase could be increased two- to nine-fold in a predictive manner.

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“…As shown by Jansons and Phillips (1990), the excluded volume between object i and j is given as follows:…”

Section: Theoretical Aspects Excluded-volume Theorymentioning

confidence: 99%

Concentration of mammalian genomic DNA using two‐phase aqueous micellar systems

Mashayekhi

Meyer

Shiigi

et al. 2008

Biotech & Bioengineering

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“…The theory can be applied to nonspherical solutes by using the appropriate expressions for V i , S i , and M i in evaluating U i j and γ i j . The necessary information for prolate and oblate spheroids (and certain other shapes) is provided by Jansons and Phillips (22). A prolate (rod-like) spheroid i is characterized by the three semiaxes r i , r i , and η i r i , where η i > 1; for an oblate (disk-like) spheroid, η i < 1.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…In order to implement the excluded volume approach for solutes of arbitrary shape, a general expression for U i j is required. As given in Jansons and Phillips (22), [14] where V i is the volume, S i is the surface area, and M i is the integral of the local mean curvature over the surface, all for object i. With this expression, partition coefficients for any set of particles can be calculated for an arbitrary fibrous or porous membrane.…”

Section: Theoretical Developmentmentioning

confidence: 99%

Effects of Multisolute Steric Interactions on Membrane Partition Coefficients

Lazzara¹,

Blankschtein²,

Deen

2000

Journal of Colloid and Interface Science

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“…7 Next, it is of some interest to compute the cross coefficient in case water is no longer a very good solvent for the polymer (i.e. < A K 3 ).…”

mentioning

confidence: 99%

Protein−Macromolecule Interactions

Odijk

1996

Macromolecules

117

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Although the interactions between proteins and various types of macromolecules are of considerable technological interest, 1 little theoretical work has been done that makes use of the fact that proteins are often comparatively small particles. Thus, our interest is in a regime opposite to that focused on in the usual depletion theories. 2 Here, a protein will be viewed, perhaps naively, as a small hard sphere whose dielectric permittivity is negligible compared to that of water. Its interaction otherwise with some macromolecular segment will be inert. Some time ago, de Gennes already presented several, not so widely known, preliminary calculations of a spherical particle interacting with a semidilute solution of polymers. 3 One supposition he made concerning the irrelevance of a certain scale, will be proved here. My aim is to present a scaling analysis of the interaction between a small sphere and a macromolecule, particularly in dilute solution. Though obviously of restricted validity, the expressions derived may prove helpful in qualitatively understanding phase separation phenomena occurring in nondilute suspensions.We first consider a protein sphere of radius a immersed in an aqueous solution containing a semidilute polymer which is well soluble. Its Kuhn length is A K , and the excluded volume between two segments is ) A K 3 . In a self-consistent field approximation, the polymer segment density ψ 2 (r b) at position r b is given by 2 where the origin is at the center of the sphere, is an eigenvalue, and ψ must tend to zero at the protein surface (r ) a). Without solving eq 1, I wish to investigate the nature of the depletion layer surrounding the protein. Far from the sphere, the concentration ψ 2 asymptotes toward a constant c o , the bulk concentration of Kuhn segments, so we conveniently introduce ψ ≡ c o 1/2 f and eq 1 becomes Here, the correlation length ≡ A K (3 c o ) -1/2 is supposed to be larger than the radius a, a condition easily realizable in practice. Assuming spherical symmetry and setting r ≡ aR, one is faced with finding the solution f ) f(R,a/ ) to with boundary conditions f ) 0 at R ) 1 and f ) 1 at R ) ∞. For an infinitesimally small sphere, we have simply which implies the depletion layer around the sphere is approximately of size a. Moreover, the second and third terms in eq 3 are straightforward regular perturbations for a , . Hence, eq 4 remains valid within a zero-order approximation, even when a > 0 provided a , . We conclude that the scale of the depletion layer for a small sphere is given solely by its radius a and does not involve at all, at least to the leading order. The irrelevancy of (assumed earlier 3 ) is nontrivial for it is circumstantial. Note that an improved theorysa hybrid approach combining scaling and self-consistent arguments as in the theory of polymer adsorption 4 swould not alter this conclusion. One would require a correlation length ∼ c o -3/4 from scaling theory instead of ∼ c o -1/2 and hence replace f 3 in eq 3 by f 4 .We now rederive a previous result 3...

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On the application of geometric probability theory to polymer networks and suspensions, I

Cited by 43 publications

References 20 publications

Concentration of mammalian genomic DNA using two‐phase aqueous micellar systems

Concentration of mammalian genomic DNA using two‐phase aqueous micellar systems

Effects of Multisolute Steric Interactions on Membrane Partition Coefficients

Protein−Macromolecule Interactions

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