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: 842; Downloads: 13
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2. Differential scanning calorimetry of proteins and Zimm–Bragg model in waterKnarik Yeritsyan, Artem Badasyan, 2019, original scientific article Abstract: Differential Scanning Calorimetry (DSC) is a regular and powerful tool to measure the specific heat profile of various materials. Hydrogen bonds play a crucial role in stabilizing the three-dimensional structure of proteins. Naturally, information about the strength of hydrogen bonds is contained in the measured DSC profiles. Despite its obvious importance, there is no approach that would allow the extraction of such information from the heat capacity measurements. In order to connect the measured profile to microscopic properties of a polypeptide chain, a proper model is required to fit. Using recent advances in the Zimm–Bragg (ZB) theory of protein folding in water, we propose a new and efficient algorithm to process the DSC experimental data and to extract the H-bonding energy among other relevant constants. Thus, for the randomly picked set of 33 proteins, we have found a quite narrow distribution of hydrogen bonding energies from 1 to 8 kJ/mol with the average energy of intra-protein hydrogen bonds kJ/mol and the average energy of water–protein bonds as kJ/mol. This is an important illustration of a tiny disbalance between the water–protein and intraprotein hydrogen bonds. Fitted values of the nucleation parameter belong to the range from 0.001 to 0.01, as expected. The reported method can be considered as complementary to the classical two-state approach and together with other parameters provides the protein–water and intraprotein H-bonding energies, not accessible within the two-state paradigm.
Keywords: protein folding, differential scanning calorimetry, heat capacity, two-state model, Hawley model
Published in RUNG: 26.08.2024; Views: 1440; Downloads: 4
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4. Differential scanning calorimetry of proteins and the two-state model : comparison of two formulasKnarik Yeritsyan, Artem Badasyan, 2024, original scientific article 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: 1949; Downloads: 11
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5. 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: 2949; Downloads: 0
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6. Spin model of water and post-processing of protein folding experimentsArtem Badasyan, Knarik Yeritsyan, 2023, published scientific conference contribution abstract 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: 2486; Downloads: 7
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7. Potts spins, protein conformations and implicit water modelArtem 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: 3261; Downloads: 9
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8. 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: 3400; Downloads: 0
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10. Implicit water model within the Zimm-Bragg approach to analyze experimental data for heat and cold denaturation of proteinsArtem 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: 3621; Downloads: 17
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