Macromolecule persistence length model

The anisotropy of the coil has been calculated for other models of the macromolecule. Expressions for the anisotropy coefficient are known in the case where the macromolecule has been represented schematically by a continuous thread (the persistence length model) (Gotlib 1964 Zgaevskii and Pokrovskii 1970) and also in the case where the microstructure of the macromolecules has been specified. In the latter case, the anisotropy coefficient of the macromolecule is expressed in terms of the bond polarisabilities and other microcharacteristics of the macromolecule (Flory 1969). 

A theoretical approach is applied to elucidate the molecular conformations, associated flexibility, and dynamics of polylp-hydroxybenzoic acid) esters, pHB. Properties such as the radius of gyration and persistence length which are characteristic for the stiffness of a macromolecule are calculated on the basis of two different theoretical methods (a) Molecular dynamics and (b) the RIS model augmented by the more recent scheme for the matrix computations. The analysis of the results obtained by the latter method reflects a strong dependence on the choice of the structural parameters of the system. 

The last relation shows that a long macromolecule rolls up into a coil at high temperatures. The smaller the elasticity coefficient a is, the more it coils up. Another name for the model of flexible thread is the model of persistence length or the Kratky-Porod model. The quantity a/T is called the persistence length (Birshtein and Ptitsyn 1966). 

The conformation of macromolecules in linear polymers can be characterized by the vector h which connects the chain ends (end-to-end vector). For rigid-chain polymers the conformation of macromolecules is usually described by the persistence length a (worm-Uke chain model) which is related to /i as ... 

In summary, the MRG-CG procedure is a systematic and reliable general approach to optimizing the interactions potentials for DNA and ions, reproducing important physical observables that characterize the Hamiltonian itself. This, in turn, leads to the similarity of the structural fluctuations of the macromolecule obtained from the CG and fully atomistic simulations. Application of this technique to coarse-graining DNA molecules resulted in a model that can be used reliably describe the DNA s structural dynamics, including complex anharmonic local deformations of the DNA chains. Likewise, this model also accurately describes the distribution of mobile ions around the DNA molecules and reproduces the experimentally measured dependence of DNA chain s persistence length on the solution ionic strength. 

As was pointed above, a combination of scattering techniques and model macromolecules are required to characterize independently the conformation of the backbone and side chains on different length scales. In addition to scattering measurements, AFM was used as a complementary technique to determine the persistence length of poly (iV-isopropylacrylamide) (PNIPAM) bmshes by measuring tensile forces upon stretching of tethered molecules in an aqueous solution. 

Here, we report on single-molecule stretching of native fibronectin and the influence of the compatible solutes ectoine and sarcosine on the mechanical properties, as revealed by the unfolding of the individual subunits and the overall persistence length of the macromolecule [131], In accordance with the preferential exclusion model, we found a significant stabilization of the protein structure in the presence of osmolytes but not an increase in unfolding forces. 

Shape persistence as a basis for controllable function is one of the main features of proteins that serve as mechanical support for cofactors (e.g., chromophores in light harvesting complexes), transmit mechanical force (e.g., in muscles), or function as nanoscopic pumps in active transport of substrates through cell membranes. Transfer of this concept to the realm of functional materials is a rather recent development and the term shape persistence for synthetic macromolecules is often used with the loose meaning of relatively rigid compared to most synthetic polymers. For linear polymers, shape persistence can be quantified by the persistence length Lp if one assumes that residual flexibility conforms to the worm-like chain (WLC) model. This assumption has been rarely tested and for many synthetic polymers Lp is either unknown or known with rather limited precision. 

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