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2. Differential scanning calorimetry of proteins and the two-state model : comparison of two formulasKnarik Yeritsyan, Artem Badasyan, 2024, izvirni znanstveni članek Opis: 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. Ključne besede: protein folding, differential scanning calorimetry, heat capacity, two-state model, Hawley model Objavljeno v RUNG: 21.05.2024; Ogledov: 590; Prenosov: 3 Celotno besedilo (380,96 KB) Gradivo ima več datotek! Več... |
3. 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: 1163; Prenosov: 0 Gradivo ima več datotek! Več... |
4. Spin model of water and post-processing of protein folding experimentsArtem Badasyan, Knarik Yeritsyan, 2023, objavljeni povzetek znanstvenega prispevka na konferenci Opis: 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. Ključne besede: spin model, water, protein folding Objavljeno v RUNG: 04.09.2023; Ogledov: 1180; Prenosov: 7 Celotno besedilo (1,47 MB) Gradivo ima več datotek! Več... |
5. 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: 1491; Prenosov: 7 Povezava na datoteko Gradivo ima več datotek! Več... |
6. 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: 1659; Prenosov: 0 Gradivo ima več datotek! Več... |
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8. 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: 2440; Prenosov: 15 Povezava na celotno besedilo Gradivo ima več datotek! Več... |
9. The finite size effects and two-state paradigm of protein foldingArtem Badasyan, Matjaž Valant, Jože Grdadolnik, Vladimir N. Uversky, 2021, izvirni znanstveni članek Opis: The coil to globule transition of the polypeptide chain is the physical phenomenon behind the folding of globular proteins. Globular proteins with a single domain usually consist of about 30 to 100 amino acid residues, and this finite size extends the transition interval of the coil-globule phase transition. Based on the pedantic derivation of the two-state model, we introduce the number of amino acid residues of a polypeptide chain as a parameter in the expressions for two cooperativity measures and reveal their physical significance. We conclude that the k2 measure, defined as the ratio of van ’t Hoff and calorimetric enthalpy is related to the degeneracy of the denatured state and describes the number of cooperative units involved in the transition; additionally, it is found that the widely discussed k2=1 is just the necessary condition to classify the protein as the two-state folder. We also find that Ωc, a quantity not limited from above and growing with system size, is simply proportional to the square of the transition interval. This fact allows us to perform the classical size scaling analysis of the coil-globule phase transition. Moreover, these two measures are shown to describe different characteristics of protein folding Ključne besede: protein folding, two-state model, size scaling, thermodynamic cooperativity Objavljeno v RUNG: 24.02.2021; Ogledov: 2453; Prenosov: 69 Povezava na celotno besedilo Gradivo ima več datotek! Več... |
10. Water reveals non-Arrhenius kinetics in protein folding experimentsArtem Badasyan, 2020, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje) Opis: 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 Ključne besede: water, protein folding, non-Arrhenius kinetics Objavljeno v RUNG: 20.07.2020; Ogledov: 2998; Prenosov: 112 Celotno besedilo (2,35 MB) |