1. Modeling of solvent role in protein folding experiments : dissertationKnarik Yeritsyan, 2025, doktorska disertacija Opis: 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. Ključne besede: 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 Objavljeno v RUNG: 27.01.2025; Ogledov: 300; Prenosov: 10
Celotno besedilo (5,12 MB) |
2. Modelling water for calorimetry of proteinsKnarik Yeritsyan, Artem Badasyan, 2023, objavljeni povzetek znanstvenega prispevka na konferenci Opis: 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. Ključne besede: Zimm-Bragg model, water model, helix-coil transition, protein folding, differential scanning calorimetry Objavljeno v RUNG: 18.10.2023; Ogledov: 2275; Prenosov: 0 Gradivo ima več datotek! Več... |
3. Potts spins, protein conformations and implicit water modelArtem Badasyan, 2023, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje) Opis: 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. Ključne besede: protein folding, Zimm-Bragg, protein-water interactions Objavljeno v RUNG: 19.06.2023; Ogledov: 2652; Prenosov: 8
Povezava na datoteko Gradivo ima več datotek! Več... |
4. Spin Model of Protein Conformations in water: Theory vs Experiment.Artem Badasyan, Knarik Yeritsyan, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje) Opis: 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). Ključne besede: Protein folding, CD, DSC, Zimm-Bragg Objavljeno v RUNG: 15.05.2023; Ogledov: 2984; Prenosov: 0 Gradivo ima več datotek! Več... |
5. |
6. |
7. |
8. System size dependence in the Zimm-Bragg model : partition function limits, transition temperature and intervalArtem Badasyan, 2021, izvirni znanstveni članek Opis: 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. Ključne besede: Zimm-Bragg model, helix-coil transition, zipper model Objavljeno v RUNG: 17.06.2021; Ogledov: 3445; Prenosov: 87
Povezava na celotno besedilo Gradivo ima več datotek! Več... |
9. 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, izvirni znanstveni članek Opis: 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. Ključne besede: protein folding, cold denaturation, water, Zimm-Bragg model Objavljeno v RUNG: 06.05.2021; Ogledov: 3235; Prenosov: 16
Povezava na celotno besedilo Gradivo ima več datotek! Več... |
10. New method to process Circular Dichroism experimental data on heat and cold denaturation of polypeptides in waterArtem Badasyan, Matjaž Valant, 2018, objavljeni povzetek znanstvenega prispevka na konferenci Opis: 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) Ključne besede: Biopolymers, Circular Dichroism, Zimm-Bragg model, helix-coil transition. Objavljeno v RUNG: 22.10.2018; Ogledov: 5266; Prenosov: 0 Gradivo ima več datotek! Več... |