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Abstract: Differential Scanning Calorimetry (DSC) is a regular and powerful tool to measure the specific heat profile of various materials. In order to connect the measured profile to the properties of a particular protein, a model is required to fit. We discuss here the application of an exact two-state formula with its approximation and process the DSC experimental data on protein folding in water. The approximate formula relies on the smallness of the transition interval, which is different for each protein. With an example of the set of 33 different proteins, we show the practical validity of the approximation and the equivalence of exact and approximate two-state formulas for processing DSC data.
Keywords: protein folding, differential scanning calorimetry, heat capacity, two-state model, Hawley model
Published in RUNG: 21.05.2024; Views: 352; Downloads: 3
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Abstract: The presence of several distinct minima in nearest-neighbor potentials in polymers makes it possible to describe polymer conformations in terms of discrete isomeric states, naturally leading to spin language. Using this general approach, a decade ago we have suggested the Hamiltonian formulation for the Zimm and Bragg model of protein conformations [1,2]. Later we have augmented the model by an oversimplified spin model for water, resulting in both cold and hot denaturations [3]. We construct the Statistical Mechanics for the model and get access to its Thermodynamics. Resulting order parameter and specific heat expressions are successfully fit to available experimental data [4]. Thanks to solid and traceable theoretical foundations, the procedure provides better quality fits as compared to the state-of-the-art two-state model, routinely used to process protein folding experiments.
Keywords: spin model, water, protein folding
Published in RUNG: 04.09.2023; Views: 999; Downloads: 7
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Abstract: Background (approx. 70 words) I will overview the application of spin models of Statistical Mechanics to describe polypeptide conformations. Zimm and Bragg model is one of the most successful examples of such approach [1]. In 2010 we have suggested the microscopic formulation of the model [2], which was later augmented by including the interactions with water [3]. Adding the solvent opened doors for the direct comparisons with UV-vis, Circular Dichroism (CD) and Differential Scanning Calorimetry (DSC) experiments. Aim (approx. 30 words) Based on a statistical Potts-like spin model of protein folding we provide formulas for experimentally measurable quantities and report a perfect fit. Our approach suggest a new method to process the results of protein folding experiments. Method (approx. 100 words) We start from the microscopic Hamiltonian formulation of the polypeptide model in water and use the usual Statistical Mechanics route from the model to partition function and the thermodynamics. Using Mayer expansion and summation over the solvent degrees of freedom, the problem is shown to be equivalent to in vacuo model with some effective, temperature dependent interaction energy. Estimated partition function leads to the expressions for the thermodynamic potentials and order parameter averages. The comparison (least-square fit) with the experimental data points from CD and DSC experiments on protein folding allows to extract the information on hydrogen bonding strengths, not available with the classical approach. Results & Discussion (approx 200 words, or less if you paste an image or insert a table ) Proposed model allows for the cold denaturation under certain well-defined conditions. The agreement between the theoretical curves and data points is excellent, and the values of fitted parameters are within the expected ranges. The limitations of the approach are naturally related to the limitations of the Zimm-Bragg original model, intended to describe the changes of the secondary structure elements only. Taking into account that the so-called “two-state” model widely used nowadays to process the experiment does not contain any info regarding the hydrogen bonding energies, the method we suggest provides a promising alternative. Conclusion (70 words approximately) The proposed approach does what it is intended to do: processing of the experimental data on protein folding. However the model contains the very same serious limitations, as the two-state model: it is oversimplified in many respects. Whether the currently available experimental methods need a better model than already suggested ones or not, is an open question. References: [1] Zimm, B.H.; Bragg, J.K.; J. Chem. Phys. 31:526–535 (1959). [2] Badasyan, A.V. et al., Phys. Rev. E 81:021921 (2010). [3] Badasyan, A.V. et al., Phys. Rev. E 89:022723 (2014). [4] Badasyan, A. et al.; Eur.Phys. J. E 36:1–9 (2013).
Keywords: Protein folding, CD, DSC, Zimm-Bragg
Published in RUNG: 15.05.2023; Views: 1508; Downloads: 0
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Abstract: Studies of biopolymer conformations essentially rely on theoretical models that are routinely used to process and analyze experimental data. While modern experiments allow study of single molecules in vivo, corresponding theories date back to the early 1950s and require an essential update to include the recent significant progress in the description of water. The Hamiltonian formulation of the Zimm-Bragg model we propose includes a simplified, yet explicit model of water-polypeptide interactions that transforms into the equivalent implicit description after performing the summation of solvent degrees of freedom in the partition function. Here we show that our model fits very well to the circular dichroism experimental data for both heat and cold denaturation and provides the energies of inter- and intra- molecular H-bonds, unavailable with other processing methods. The revealed delicate balance between these energies determines the conditions for the existence of cold dena- turation and thus clarifies its absence in some proteins.
Keywords: protein folding, cold denaturation, water, Zimm-Bragg model
Published in RUNG: 06.05.2021; Views: 2275; Downloads: 15
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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: 2831; Downloads: 112
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