1. Modeling of solvent role in protein folding experiments : dissertationKnarik Yeritsyan, 2025, doctoral dissertation Abstract: The Zimm-Bragg (ZB) model serves as a fundamental framework for elucidating conformational transitions in biopolymers, offering simplicity and efficacy in processing experimental data. This study provides a comprehensive review of the Zimm-Bragg model and its Hamiltonian formulation, with particular emphasis on incorporating water interactions and chain size effects into the computational framework. We propose a modified ZB model that accounts for water-polypeptide interactions, demonstrating its ability to describe phenomena such as cold denaturation and helix-coil transitions. In the realm of NanoBioTechnologies, the manipulation of short polypeptide chains is commonplace. Experimental investigation of these chains in vitro often relies on techniques like Circular Dichroism (CD) and timeresolved infrared spectroscopy. Determining interaction parameters necessitates processing the temperature dependence of the normalized degree of helicity through model fitting. Leveraging recent advancements in the Hamiltonian formulation of the Zimm and Bragg model, we explicitly incorporate chain length and solvent effects into the theoretical description. The resulting expression for helicity degree adeptly fits experimental data, yielding hydrogen bonding energies and nucleation parameter values consistent with field standards. Differential Scanning Calorimetry (DSC) stands as a potent tool for measuring the specific heat profile of materials, including proteins. However, relating the measured profile to microscopic properties requires a suitable model for fitting. We propose a novel algorithm for processing DSC experimental data based on the ZB theory of protein folding in water. This approach complements the classical two-state paradigm and provides insights into protein-water and intraprotein hydrogen bonding energies. An analytical expression for heat capacity, considering water interaction, is derived and successfully applied to fit numerous DSC experimental datasets reported in the literature. Additionally, we compare this approach with the classical two-state model, demonstrating its efficacy in fitting DSC data. Furthermore, we have developed and launched a free online tool for processing CD and DSC experimental data related to protein folding, aiming to support scientific research.
Keywords: Zimm-Bragg model, conformational transitions, helix-coil transitions, cold denaturation, circular dichroism, differential scanning calorimetry, protein folding, water-protein interaction, hydrogen bonding energy, degree of helicity, short polypeptide chains, protein heat capacity, protein data analysis, dissertations
Published in RUNG: 27.01.2025; Views: 465; Downloads: 10
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2. Modelling water for calorimetry of proteinsKnarik Yeritsyan, Artem Badasyan, 2023, published scientific conference contribution abstract Abstract: Differential Scanning Calorimetry (DSC) is a powerful technique used to study the thermal stability and unfolding of proteins. DSC provides the excess heat capacity profile and is used to study the thermodynamics of a given protein. By fitting DSC data to the model, researchers can obtain valuable information about the thermodynamics of protein folding and unfolding, which can help them better understand protein structure, stability, and function.
Based on Hamiltonian representation of ZB model and using the solvent effects we derived an expression for heat capacity in proteins and successfuly fit it to experimental data. As we show, our model provides a better fit to experimental data, as compared to the 2-state model. The model we propose takes into account also water effects and we show that it fits better to experimental data giving inter- and intra-molecular H-bonding energies instead of reporting only one total enthalpy.
Keywords: Zimm-Bragg model, water model, helix-coil transition, protein folding, differential scanning calorimetry
Published in RUNG: 18.10.2023; Views: 2514; Downloads: 0
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6. System size dependence in the Zimm-Bragg model : partition function limits, transition temperature and intervalArtem 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: 3585; Downloads: 88
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7. On spin description of water-biopolymer interactions: theory and experiment of reentrant order-disorder transition.Artem Badasyan, invited lecture at foreign university Abstract: The experimental studies of biopolymer conformations have reached an unprecedented level of
detailization during the past decade and allow now 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.
Keywords: helix-coil transition, water-polypeptide interactions
Published in RUNG: 13.03.2019; Views: 4370; Downloads: 0
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8. New method to process Circular Dichroism experimental data on heat and cold denaturation of polypeptides in waterArtem 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 (artem.badasyan@ung.si)
Keywords: Biopolymers, Circular Dichroism, Zimm-Bragg model, helix-coil transition.
Published in RUNG: 22.10.2018; Views: 5455; Downloads: 0
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9. Physics behind the Conformational Transitions in Biopolymers. Demystification of DNA melting and Protein FoldingArtem Badasyan, invited lecture at foreign university Abstract: Biophysics is the area of research, devoted to the studies of physical problems related to living systems. Animal cell is the smallest unit of an organism and mainly contains water solutions of structurally inhomogeneous polymers of biological origin: polypeptides (proteins) and polynucleotides (DNA, RNA). Statistical physics of macromolecules allows to describe the conformations of both synthetic and bio-polymers and constitutes the basis of Biophysics. During the talk I will report on the biophysical problems I have solved with numerical simulations (Langevin-based Molecular Dynamics of Go-like protein folding model and Monte Carlo with Wang-Landau sampling) and analytical studies of spin models (formula evaluation by hand, enforced with computer algebra systems). The direct connections with the theory of phase transitions, algebra of non-commutative operators and decorated spin models will be elucidated.
Keywords: Biophysics, protein folding, helix-coil transition, spin models
Published in RUNG: 13.12.2016; Views: 7219; Downloads: 0
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