ALBERT

Description: There is an opinion in professional literature that edge-strands in β-sheet are critical to the processes of amyloid transformation. Propagation of fibrillar forms mainly takes place on the basis of β-sheet type interactions. In many proteins, the edge strands represent only a partially matched form to the β-sheet. Therefore, the edge-strand takes slightly distorted forms. The assessment of the level of arrangement can be carried out based on studying the secondary structure as well as the structure of the hydrophobic core. For this purpose, a fuzzy oil drop model was used to determine the contribution of each fragment with a specific secondary structure to the construction of the system being the effect of a certain synergy, which results in the construction of a hydrophobic core. Studying the participation of β-sheets edge fragments in the hydrophobic core construction is the subject of the current analysis. Statuses of these edge fragments in β-sheets in ferredoxin-like folds are treated as factors that disturb the symmetry of the system.

Description: The issue of changing the structure of globular proteins into an amyloid form is in the focus of researchers' attention. Numerous experimental studies are carried out, and mathematical models to define the essence of amyloid transformation are sought. The present work focuses on the issue of the hydrophobic core structure in amyloids. The form of ordering the hydrophobic core in globular proteins is described by a 3D Gaussian distribution analog to the distribution of hydrophobicity in a spherical micelle. Amyloid fibril is a ribbon-like micelle made up of numerous individual chains, each representing a flat structure. The distribution of hydrophobicity within a single chain included in the fibril describes the 2D Gaussian distribution. Such a description expresses the location of polar residues on a circle with a center with a high level of hydrophobicity. The presence of this type of order in the amyloid forms available in Preotin Data Bank (PDB) (both in proto- and superfibrils) is demonstrated in the present work. In this system, it can be assumed that the amyloid transformation is a chain transition from 3D Gauss ordering to 2D Gauss ordering. This means changing the globular structure to a ribbon-like structure. This observation can provide a simple mathematical model for simulating the amyloid transformation of proteins.

Description: Protein structure is the result of the high synergy of all amino acids present in the protein. This synergy is the result of an overall strategy for adapting a specific protein structure. It is a compromise between two trends: The optimization of non-binding interactions and the directing of the folding process by an external force field, whose source is the water environment. The geometric parameters of the structural form of the polypeptide chain in the form of a local radius of curvature that is dependent on the orientation of adjacent peptide bond planes (result of the respective Phi and Psi rotation) allow for a comparative analysis of protein structures. Certain levels of their geometry are the criteria for comparison. In particular, they can be used to assess the differences between the structural form of biologically active proteins and their amyloid forms. On the other hand, the application of the fuzzy oil drop model allows the assessment of the role of amino acids in the construction of tertiary structure through their participation in the construction of a hydrophobic core. The combination of these two models—the geometric structure of the backbone and the determining of the participation in the construction of the tertiary structure that is applied for the comparative analysis of biologically active and amyloid forms—is presented.

Description: The model, describing a method of determining the structure of an early intermediate in the process of protein folding to analyze nonredundant PDB protein bases, allows determining the relationship between the sequence of tetrapeptides and their structural forms expressed by structural codes. The contingency table expressing such a relationship can be used to predict the structure of polypeptides by proposing a structural form with a precision limited to the structural code. However, by analyzing structural forms in native forms of proteins based on the fuzzy oil drop model, one can also determine the status of polypeptide chain fragments with respect to the assumptions of this model. Whether the probability distributions for both compliant and noncompliant forms were similar or whether the tetrapeptide sequences showed some differences at a level of a set of structural codes was investigated. The analysis presented here indicated that some sequences in both forms revealed differences in probability distributions expressed as a negative statistically significant correlation coefficient. This meant that the identified sections (tetrapeptides) took different forms against the fuzzy oil drop model. It may suggest that the information of the final status with respect to hydrophobic core formation is already carried by the structure of the early-stage intermediate.

Description: Four de novo proteins differing in single mutation positions, with a chain length of 56 amino acids, represent diverse 3D structures: monomeric 3α and 4β + α folds. The reason for this diversity is seen in the different structure of the hydrophobic core as a result of synergy leading to the generation of a system in which the polypeptide chain as a whole participates. On the basis of the fuzzy oil drop model, where the structure of the hydrophobic core is expressed by means of the hydrophobic distribution function in the form of a 3D Gaussian distribution, it has been shown that the composition of the hydrophobic core in these two structural forms is different. In addition, the use of a model to determine the structure of the early intermediate in the folding process allows to indicate differences in the polypeptide chain geometry, which, combined with the construction of a common hydrophobic nucleus as an effect of specific synergy, may indicate the reason for the diversity of the folding process of the polypeptide chain. The results indicate the need to take into account the presence of an external force field originating from the water environment and that its active impact on the formation of a hydrophobic core whose participation in the stabilization of the tertiary structure is fundamental.

Description: Research on the protein folding problem differentiates the protein folding process with respect to the duration of this process. The current structure encoded in sequence dogma seems to be clearly justified, especially in the case of proteins referred to as fast-folding, ultra-fast-folding or downhill. In the present work, an attempt to determine the characteristics of this group of proteins using fuzzy oil drop model is undertaken. According to the fuzzy oil drop model, a protein is a specific micelle composed of bi-polar molecules such as amino acids. Protein folding is regarded as a spherical micelle formation process. The presence of covalent peptide bonds between amino acids eliminates the possibility of free mutual arrangement of neighbors. An example would be the construction of co-micelles composed of more than one type of bipolar molecules. In the case of fast folding proteins, the amino acid sequence represents the optimal bipolarity system to generate a spherical micelle. In order to achieve the native form, it is enough to have an external force field provided by the water environment which directs the folding process towards the generation of a centric hydrophobic core. The influence of the external field can be expressed using the 3D Gaussian function which is a mathematical model of the folding process orientation towards the concentration of hydrophobic residues in the center with polar residues exposed on the surface. The set of proteins under study reveals a hydrophobicity distribution compatible with a 3D Gaussian distribution, taken as representing an idealized micelle-like distribution. The structure of the present hydrophobic core is also discussed in relation to the distribution of hydrophobic residues in a partially unfolded form.

Description: The water environment determines the activity of biological processes. The role of such an environment interpreted in the form of an external field expressed by the 3D Gaussian distribution in the fuzzy oil drop model directs the folding process towards the generation of a centrally located hydrophobic core with the simultaneous exposure of polar residues on the surface. In addition to proteins soluble in the water environment, there is a significant group of membrane proteins that act as receptors or channels, including ion channels in particular. The change of the polar (water) environment into a highly hydrophobic (membrane) environment is quite radical, resulting in a different hydrophobicity distribution within the membrane protein. Modification of the notation of the force field expressing the presence of the hydrophobic environment has been proposed in this work. A modified fuzzy oil drop model with its adaptation to membrane proteins was used to interpret the structure of membrane proteins–mechanosensitive channel. The modified model was also used to describe the so-called negative cases—i.e., for water-soluble proteins with a clear distribution consistent with the fuzzy oil drop model.

Description: The two forms of transthyretin differing slightly in the tertiary structure, despite the presence of five mutations, show radically different properties in terms of susceptibility to the amyloid transformation process. These two forms of transthyretin are the object of analysis. The search for the sources of these differences was carried out by means of a comparative analysis of the structure of these molecules in their native and early intermediate stage forms in the folding process. The criterion for assessing the degree of similarity and differences is the status of the hydrophobic core. The comparison of the level of arrangement of the hydrophobic core and its initial stages is possible thanks to the application of divergence entropy for the early intermediate stage and for the final forms. It was shown that the minimal differences observed in the structure of the hydrophobic core of the forms available in PDB, turned out to be significantly different in the early stage (ES) structure in folding process. The determined values of divergence entropy for both ES forms indicate the presence of the seed of hydrophobic core only in the form resistant to amyloid transformation. In the form of aggressively undergoing amyloid transformation, the structure lacking such a seed is revealed, being a stretched one with a high content of β-type structure. In the discussed case, the active presence of water in the structural transformation of proteins expressed in the fuzzy oil drop model (FOD) is of decisive importance for the generation of the final protein structure. It has been shown that the resistant form tends to generate a centric hydrophobic core with the possibility of creating a globular structure, i.e., a spherical micelle-like form. The aggressively transforming form reveals in the structure of its early intermediate, a tendency to form the ribbon-like micelle as observed in amyloid.