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Abstract: Within the recently developed Hamiltonian formulation of the Zimm and Bragg model we re-evaluate several size dependent approximations of model partition function. Our size analysis is based on the comparison of chain length N with the maximal correlation (persistence) length ξ of helical conformation. For the first time we re-derive the partition function of zipper model by taking the limits of the Zimm–Bragg eigenvalues. The critical consideration of applicability boundaries for the single-sequence (zipper) and the long chain approximations has shown a gap in description for the range of experimentally relevant chain lengths of 5–10 persistence lengths ξ. Correction to the helicity degree expression is reported. For the exact partition function we have additionally found, that: at N/ξ ≈ 10 the transition temperature T m reaches its asymptotic behavior of infinite N; the transition interval ∆T needs about a thousand persistence lengths to saturate at its asymptotic, infinite length value. Obtained results not only contribute to the development of the Zimm–Bragg model, but are also relevant for a wide range of Biotechnologies, including the Biosensing applications.
Keywords: Zimm-Bragg model, helix-coil transition, zipper model
Published in RUNG: 17.06.2021; Views: 3319; Downloads: 87
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Abstract: The coil to globule transition of the polypeptide chain is the physical phenomenon behind the folding of globular proteins. Globular proteins with a single domain usually consist of about 30 to 100 amino acid residues, and this finite size extends the transition interval of the coil-globule phase transition. Based on the pedantic derivation of the two-state model, we introduce the number of amino acid residues of a polypeptide chain as a parameter in the expressions for two cooperativity measures and reveal their physical significance. We conclude that the k2 measure, defined as the ratio of van ’t Hoff and calorimetric enthalpy is related to the degeneracy of the denatured state and describes the number of cooperative units involved in the transition; additionally, it is found that the widely discussed k2=1 is just the necessary condition to classify the protein as the two-state folder. We also find that Ωc, a quantity not limited from above and growing with system size, is simply proportional to the square of the transition interval. This fact allows us to perform the classical size scaling analysis of the coil-globule phase transition. Moreover, these two measures are shown to describe different characteristics of protein folding
Keywords: protein folding, two-state model, size scaling, thermodynamic cooperativity
Published in RUNG: 24.02.2021; Views: 3112; Downloads: 71
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Abstract: Statistical theories describe systems in equilibrium, and cannot be used to study kinetics. However, the theo- ries are based on coarse-grained parameters, that include assumptions regarding the underlying kinetics. If such assumptions are incorrect, the theoretical expressions, used to process the experimental data, will not fit. I report on one such case we have met within the application of Zimm-Bragg [1] theory to process folding experiments, and discuss the reasons and consequences. Studies of relaxation phenomena in glass-forming liquids by default account for the shift in temperature by some value, corresponding to the glass formation temperature, .In particular, temperature shift appears in hydrated proteins because of the presence of partially glassy states giving rise to non- Arrhenius relaxation times log τ ~ [2]. A phenomenological approach was suggested by Adam and Gibbs as early as in 1965 to describe the sudden increase of viscosity and the slowing down of the collective modes in super-cooled liquids as the temperature is approaching[3]. The key idea of Adam-Gibbs theory was to consider the supercooled liquid as a set of clusters (cooperatively rearranging regions) of different sizes that change with temperature, giving rise to the shift in re- laxation time. The temperature shift factor is present in many theories describing properties of water. Thus, Truskett and Dill had to include the Adamm-Gibbs temperature shift into their simple analytical model of water to achieve the agreement with experimental data on the tem- perature dependence of self-diffusion coefficient [4]. Later, Schiro and Weik have summarised recent in vitro and in silico experimental results regarding the role of hydration water in the onset of protein structural dy- namics, and have reported the presence of super-Arrhenius relaxation region above the ”protein dynamic transition” temperature [4]. Recently, Mallamace et al have used the Adam-Gibbs theory in their NMR meas- urements of protein folding-unfolding in water [4] and to rationalise the complicated pressure-temperature diagrams in these glass-forming systems. Motivated by the considerations above, and taking into account the relationship between the unimolecular rate of folding in water and the relaxation time 45 , we introduce the tem- perature shift into the formulas used to fit experimental data on hydrated polypeptides. By doing so we resolve the paradox and complete the new method of processing the Circular Dichroism ex- perimental data on protein folding
Keywords: water, protein folding, non-Arrhenius kinetics
Published in RUNG: 20.07.2020; Views: 3610; Downloads: 117
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Abstract: The attraction between the polycyclic aromatic surface elements of carbon nanotubes (CNT) and the aro- matic nucleotides of deoxyribonucleic acid (DNA) leads to reversible adsorption (physisorption) between them. With the goal to provide the theoretical support to numerous technologies on the basis of DNA-CNT hybrids, we propose a Hamiltonian formulation for the zipper model that accounts for relevant interactions and allows for the processing of experimental data, which has awaited an available theory for a decade.
Keywords: DNA, CNT
Published in RUNG: 22.05.2020; Views: 3747; Downloads: 107
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Keywords: DNA, CNT, zipper model, physisorption
Published in RUNG: 28.01.2020; Views: 3305; Downloads: 0
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