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1.
Modelling water for calorimetry of proteins
Knarik 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: 622; Downloads: 0
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2.
Spin model of water and post-processing of protein folding experiments
Artem 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: 700; Downloads: 3
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3.
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: 945; Downloads: 5
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4.
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: 1192; Downloads: 0
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5.
Finite size effects at protein folding from the two-state perspective
Artem Badasyan, Matjaž Valant, Jože Grdadolnik, Vladimir N. Uversky, 2021, published scientific conference contribution abstract

Keywords: protein folding, two-state model, finite size effects
Published in RUNG: 27.09.2021; Views: 1658; Downloads: 0
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6.
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: 2026; Downloads: 13
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7.
The finite size effects and two-state paradigm of protein folding
Artem Badasyan, Matjaž Valant, Jože Grdadolnik, Vladimir N. Uversky, 2021, original scientific article

Abstract: 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
Keywords: protein folding, two-state model, size scaling, thermodynamic cooperativity
Published in RUNG: 24.02.2021; Views: 2043; Downloads: 64
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8.
Water reveals non-Arrhenius kinetics in protein folding experiments
Artem Badasyan, 2020, published scientific conference contribution abstract (invited lecture)

Abstract: 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
Keywords: water, protein folding, non-Arrhenius kinetics
Published in RUNG: 20.07.2020; Views: 2592; Downloads: 111
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9.
Physics behind the Conformational Transitions in Biopolymers. Demystification of DNA melting and Protein Folding
Artem 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: 5690; Downloads: 0
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10.
Entropic cost of folding and phase diagrams of polypeptides: Why are IDPs unfolded at room temperature?
Artem Badasyan, invited lecture at foreign university

Abstract: In spin models, that are applied to describe the conformational transitions in polymers, the number of spin orientations, that correspond to the disordered conformation, can be estimated using fundamental definitions of Statistical Physics. For instance, when considering alpha-helix to coil transition in polypeptides, the role of generalized coordinates is played by pairs of torsional angle, and the repeating unit populates different regions of that 2D contour map, depending on conformation. By scanning over all possible torsional angles, that do not violate the obvious limitations due to the excluded volume, the so-called Ramachandran map can be plotted, which is actually the phase space visualization for the helix-coil transition problem. The region of phase space, corresponding to the ordered, helical conformations, is much more limited, than the one, corresponding to all other (allowed) conformations. We can calculate the areas of these regions as Γhelix and Γcoil , and construct the ratio Q = Γcoil . Naturally, it can be interpreted as log(Q) = Scoil − Shelix = ΔS, the entropic cost of helix with respect to coil. To illustrate the importance of the entropic price of ordered conformation we report our recent results, that allowed to explain the peculiarity of phase diagrams of Intrinsically Disordered Proteins (IDP) out of larger Q-values, as compared to globular counterparts. In particular, it has been shown, that due to larger Q, the phase diagram of IDP is shifted towards higher temperatures.
Keywords: IDP, protein folding, phase diagram
Published in RUNG: 23.06.2016; Views: 4572; Downloads: 0
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