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Potts spins, protein conformations and implicit water model
Artem Badasyan, 2023, published scientific conference contribution abstract (invited lecture)

Abstract: I will summarize past and current achievements in the field of spin model applications to protein conformations. Using classical Statistical Mechanics scheme and 1D many-body Hamiltonian, exact partition function can be estimated, giving access to the free energy, order parameter and specific heat. I will introduce a simplified water model as an additive term at the level of Hamiltonian, and will show how the solvent degrees of freedom can be summed out. The suggested procedure results in the effective Hamiltonian with the temperature dependent hydrogen bonding energy. If the many-body range is reduced to the nearest neighbour, the approach reduces to the Zimm-Bragg model. Obtained expressions for the order parameter and the specific heat nicely fit to the corresponding experiments for protein folding, providing an alternative or complementary scheme for the processing of experimental data.
Keywords: protein folding, Zimm-Bragg, protein-water interactions
Published in RUNG: 19.06.2023; Views: 339; Downloads: 3
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Spin Model of Protein Conformations in water: Theory vs Experiment.
Artem Badasyan, Knarik Yeritsyan, published scientific conference contribution abstract (invited lecture)

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: 426; Downloads: 0
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Helix-coil theory to process experimental data for short polypeptides in solvent
Knarik Yeritsyan, Matjaz Valant, Artem Badasyan, 2022, published scientific conference contribution abstract

Keywords: Zimm-Bragg model, helix-coil transition, thermal unfolding, chain length
Published in RUNG: 10.10.2022; Views: 572; Downloads: 0
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System size dependence of the Zimm-Bragg model
Artem Badasyan, 2021, published scientific conference contribution abstract

Keywords: Zimm-Bragg model, final size effects
Published in RUNG: 27.09.2021; Views: 1200; Downloads: 0
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System size dependence in the Zimm-Bragg model : partition function limits, transition temperature and interval
Artem Badasyan, 2021, original scientific article

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: 1544; Downloads: 76
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Implicit water model within the Zimm-Bragg approach to analyze experimental data for heat and cold denaturation of proteins
Artem Badasyan, Sh. A. Tonoyan, Matjaž Valant, Jože Grdadolnik, 2021, original scientific article

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: 1624; Downloads: 12
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New method to process Circular Dichroism experimental data on heat and cold denaturation of polypeptides in water
Artem Badasyan, Matjaž Valant, 2018, published scientific conference contribution abstract

Abstract: During the past decade the experimental studies of biopolymer conformations have reached an unprecedented level of detailization and allow to study single molecules in vivo [1]. Processing of experimental data essentially relies on theoretical approaches to conformational transitions in biopolymers [2]. However, the models that are currently used, originate from the early 1960's and contain several unjustified assumptions, widely accepted at that time. Thus, the view on the conformational transitions in the polypeptides as a two-state process has very limited applicability because the all-or-none transition mechanism takes place only in short polypeptides with sizes comparable to the spatial correlation length; the original formulation of Zimm-Bragg model is phenomenological and does not allow for a microscopic model for water; the implicit consideration of the water-polypeptide interactions through the ansatz about the quadratic dependence of free energy difference on temperature can only be justified through the assumption of an ideal gas with a constant heat capacity. To get rid of these deficiencies, we augment the Hamiltonian formulation [3] of the Zimm-Bragg model [4] with the term describing the water-polypeptide interactions [5]. The analytical solution of the model results in a formula, ready to be fit to Circular Dichroism (CD) data for both heat and cold denaturation. On the example of several sets of experimental data we show, that our formula results in a significantly better fit, as compared to the existing approaches. Moreover, the application of our procedure allows to compare the strengths of inter- and intra-molecular H-bonds, an information, inaccessible before. References [1] I. König, A. Zarrine-Afsar, M. Aznauryan, A. Soranno, B. Wunderlich, F. Dingfelder, J. C. Stüber, A. Plückthun, D. Nettels, B. Schuler, (2015), Single-molecule spectroscopy of protein conformational dynamics in live eukaryotic cells/Nature Methods, 12, 773-779. [2] J. Seelig, H.-J. Schönfeld, (2016), Thermal protein unfolding by differential scanning calorimetry and circular dichroism spectroscopy. Two-state model versus sequential unfolding/Quarterly Reviews of Biophysics, 49, e9, 1-24. [3] A.V. Badasyan, A. Giacometti, Y. Sh. Mamasakhlisov, V. F. Morozov, A. S. Benight, (2010), Microscopic formulation of the Zimm-Bragg model for the helix-coil transition/Physical Review E, 81, 021921. [4] B. H. Zimm, J. K. Bragg, (1959), Theory of the Phase Transition between Helix and Random Coil in Polypeptide Chains/Journal of Chemical Physics, 31, 526. [5] A. Badasyan, Sh.A. Tonoyan, A. Giacometti, R. Podgornik, V.A. Parsegian, Y.Sh. Mamasakhlisov, V.F. Morozov, (2014), Unified description of solvent effects in the helix-coil transition/Physical Review E, 89, 022723. Corresponding author: Artem Badasyan (
Keywords: Biopolymers, Circular Dichroism, Zimm-Bragg model, helix-coil transition.
Published in RUNG: 22.10.2018; Views: 2995; Downloads: 0
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Knarik Yeritsyan, 2016, undergraduate thesis

Abstract: Zimm-Bragg model is the simplest to describe the conformational transitions in biopolymers and is regularly used for preocessing the experimental data. We review the model and its Hamiltonian definition with the goal to introduce the interaction with water into the picture. We show how modified ZB model with the account of water-polypeptide interactions allows to describe both cold denaturation and helix-coil transition and derive such the formula explicitly. The obtained theoretical expression for the helicity degree contains two independent parameters that can be fitted with the experimental data to determine the parameters of cold denaturation and helix-coil transition from a single fit and for a single set of experimental data.
Keywords: Zimm-Bragg model, conformational transitions in biopolymers, cold denaturation
Published in RUNG: 28.09.2016; Views: 6565; Downloads: 259
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