The aqueous environment is a pervasive factor which, in many ways, determines the protein folding process and consequently the activity of proteins. Proteins are unable to perform their function unless immersed in water (membrane proteins excluded from this statement). Tertiary conformational stabilization is dependent on the presence of internal force fields (nonbonding interactions between atoms), as well as an external force field generated by water. The hitherto the unknown

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... of water as the aqueous environment may be elucidated by analyzing its effects on protein structure and function. Our study is based on the fuzzy oil drop model-a mechanism which describes the formation of a hydrophobic core and attempts to explain the emergence of amyloid-like fibrils. A set of proteins which vary with respect to their fuzzy oil drop status (including titin, transthyretin and a prion protein) have been selected for in-depth analysis to suggest the plausible mechanism of amyloidogenesis. Entropy 2016, 18, 351 2 of 31 homologues, and ab initio techniques (also referred to as "new fold" models) which attempt to describe the force fields involved and thus recreate the folding process itself. In all such models the influence of the aqueous environment is described in form of pair-wise interactions between atoms belonging to the protein molecule and the environment. This kind of description is highly detailed (individual atoms interacting with each other), yet surprisingly imprecise as it restricts interactions to the local neighborhood of each atom, without considering their impact on the protein as a whole. Our work attempts to relate the structure of the protein to the properties of its aqueous environment. The structuralization of water-although poorly understood [8]-may be studied from the point of view of its effects on the protein body. In the fuzzy oil drop (FOD) model the hydrophobic core emerges as a result of the structural properties of water which cause aggregation of hydrophobic residues near the center of the protein with simultaneous exposure of hydrophobic residues on its surface. Such structuralization is obviously dependent on the presence of ions, acidity (pH), proximity to other molecules (such as membranes), ionic potentials etc. Changes in these parameters -as reported according to experiments [9]-influence the structuralization of water and in consequence influence the protein folding process leading to adoption of non-native tertiary conformations. Under normal conditions, it is assumed that structuralization of water creates a characteristic environment which causes hydrophobic residues to congregate near the center of the protein and be shielded from contact with water by hydrophilic residues exposed on the proteins surface [10]. The FOD model simulates this phenomenon through extension of the original discrete oil drop [10] model by introducing a continuous hydrophobicity density distribution gradient-a 3D Gaussian [11], more recently described in [12] . The aggregation of hydrophobic residues in the central part of the molecule corresponds to values of the 3D Gaussian which peak at the geometric center of the protein and decrease along with distance from the center, becoming close to 0 on the surface. This protein surface utilized by the FOD model is not a molecular or solvent-accessible surface, but an axis-aligned ellipsoid, which forms a 3-dimensional "capsule" container for the molecule, centered on the origin of the coordinate system. If we assume that the "natural" external force field produces an ordered hydrophobic core, an interesting question emerges-can variations in this field produce alternative distributions of hydrophobicity density? We have identified several protein families in which the actual (observed) hydrophobicity density distribution very closely matches theoretical values. This includes the antifreeze [13] and downhill [14] proteins. Local discordances between the idealized and observed distributions frequently correspond to active sites: local hydrophobicity deficiencies usually suggest the presence of a ligand binding cavity [15, 16] while local excess hydrophobicity-if present on the surface of the protein-may indicate a complexation site [17, 18] . In this work we focus on a set of proteins implicated in amyloidogenesis. The spectrum of structures ranges from proteins with very low propensity for structural changes to molecules which readily undergo amyloid-like and amyloid structural changes. Human titin (1TIT) [19], with a well-ordered hydrophobic core which closely matches the predictions of the fuzzy oil drop model [20] , represents the former group. The presence of such a core is consistent with the function of titin, which -being part of muscle tissue-is subject to powerful stretching forces and must be able to revert to its original shape in the absence of deforming factors [21] [22] [23] . The presence of a well-defined hydrophobic core appears to enable the molecule to revert to its initial form when external forces disappear. The second protein, human transthyretin (1DVQ) [24] , is widely recognized as susceptible to amyloid formation, both in vitro and in vivo [24] [25] [26] [27] [28] [29] [30] [31] . This protein exhibits local deviations from the idealized hydrophobic core structure which may be treated as the seed for amyloidogenesis. Our third object of study is the SufC-SufD complex involved in iron-sulfur cluster biosynthesis (2ZU0) [32] . There are no direct reports which would relate it to amyloidogenesis. However, comparing several publications focusing on structural analysis of amyloid fibrils [33] [34] [35] [36] [37] [38] suggests that a large Entropy 2016, 18, 351 3 of 31 fragment of 2ZU0 appears to adopt an amyloid-like conformation. Accordingly, we have classified a fragment of this structure as "amyloid-like" (AmL) for the purposes of our analysis. Our study also involves a prion protein (1B10) [39] and synuclein (1XQ8) [40] , both of which are prone to amyloid aggregation. Finally, sequence analysis has been performed for the amyloid protofibrils of the Alzheimer Aβ(9-40) peptide [41] . To make the study complete, three amyloid fibrillary structures are presented: Amyloid β 1-40 Osaka mutant (22E∆) fibrils (2MVX) [42], Amyloid β 1-40 Iowa mutation N23D fibrils (2MPZ) [43] and Amyloid β 1-42 fibrils (2MXU) [44] . All of them have been studied with the use of solid-state NMR and are implicated in Alzheimer's disease. This is why the inclusion of these molecular systems is important for the hypothesis presented in this paper. Theory The fuzzy oil drop (FOD) model is a modification of the previously described oil drop model which asserts that hydrophobic residues tend to migrate to the center of the protein body while hydrophilic residues are exposed on its surface [11, 12] . A visual description of this model is presented in Figure 1A where the dark area corresponds to a highly hydrophobic "core" while light areas represent the hydrophilic "shell". The fuzzy oil drop replaces the binary discrete model with a continuous function peaking at the center of the molecule [11] ( Figure 1B) , which causes hydrophobicity density values to decrease along with distance from the center, reaching zero on the molecular surface. Visual comparison between the two models is presented on Figure 1C ,D. Entropy 2016, 18, 351 3 of 31 comparing several publications focusing on structural analysis of amyloid fibrils [33] [34] [35] [36] [37] [38] suggests that a large fragment of 2ZU0 appears to adopt an amyloid-like conformation. Accordingly, we have classified a fragment of this structure as "amyloid-like" (AmL) for the purposes of our analysis. Our study also involves a prion protein (1B10) [39] and synuclein (1XQ8) [40] , both of which are prone to amyloid aggregation. Finally, sequence analysis has been performed for the amyloid protofibrils of the Alzheimer Aβ(9-40) peptide [41] . To make the study complete, three amyloid fibrillary structures are presented: Amyloid β 1-40 Osaka mutant (22EΔ) fibrils (2MVX) [42] , Amyloid β 1-40 Iowa mutation N23D fibrils (2MPZ) [43] and Amyloid β 1-42 fibrils (2MXU) [44] . All of them have been studied with the use of solid-state NMR and are implicated in Alzheimer's disease. This is why the inclusion of these molecular systems is important for the hypothesis presented in this paper.