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Frank Biedermann, W. Nau, H. Schneider (2014)The hydrophobic effect revisited--studies with supramolecular complexes imply high-energy water as a noncovalent driving force.
Angewandte Chemie, 53 42
A. Ben-Naim (1989)Solvent‐induced interactions: Hydrophobic and hydrophilic phenomena
Journal of Chemical Physics, 90
M. Banach, B. Kalinowska, L. Konieczny, I. Roterman-Konieczna (2016)Role of Disulfide Bonds in Stabilizing the Conformation of Selected Enzymes - An Approach Based on Divergence Entropy Applied to the Structure of Hydrophobic Core in Proteins
L. Konieczny, M. Brylinski, I. Roterman-Konieczna (2006)Gauss-Function-Based Model of Hydrophobicity Density in Proteins
In silico biology, 6 1-2
S. Kullback, R. Leibler (1951)On Information and Sufficiency
Annals of Mathematical Statistics, 22
D. Doyle, Alice Lee, John Lewis, Eunjoon Kim, M. Sheng, R. MacKinnon (1996)Crystal Structures of a Complexed and Peptide-Free Membrane Protein–Binding Domain: Molecular Basis of Peptide Recognition by PDZ
M. Banach, L. Konieczny, I. Roterman-Konieczna (2012)Ligand-binding-site recognition
Olivier Roche, R. Kiyama, Charles Brooks (2001)Ligand-protein database: linking protein-ligand complex structures to binding data.
Journal of medicinal chemistry, 44 22
Jacek Dygut, B. Kalinowska, M. Banach, M. Piwowar, L. Konieczny, I. Roterman (2016)Structural Interface Forms and Their Involvement in Stabilization of Multidomain Proteins or Protein Complexes
International Journal of Molecular Sciences, 17
T. Schutzius, Stefan Jung, T. Maitra, G. Graeber, Moritz Köhme, D. Poulikakos (2015)Spontaneous droplet trampolining on rigid superhydrophobic surfaces
B. Kalinowska, M. Banach, L. Konieczny, I. Roterman-Konieczna (2015)Application of Divergence Entropy to Characterize the Structure of the Hydrophobic Core in DNA Interacting Proteins
(2012)Use of the “fuzzy oil drop” model to identify the complexation area in protein homodimers. In: Roterman I, editor. Protein folding in silico – protein folding versus protein structure prediction
M. Banach, L. Konieczny, I. Roterman-Konieczna (2012)6 – Use of the “fuzzy oil drop” model to identify the complexation area in protein homodimers
Application of divergence
Mu Gao, J. Skolnick (2012)The distribution of ligand-binding pockets around protein-protein interfaces suggests a general mechanism for pocket formation
Proceedings of the National Academy of Sciences, 109
E. Klipp, C. Wierling, Wolfram Liebermeister (1994)Systems Biology
(2012)Ligand-binding site recognition. In: Roterman I, editor. Protein folding in silico – protein folding versus protein structure prediction
M. Banach, L. Konieczny, I. Roterman (2018)Why do antifreeze proteins require a solenoid?
IntroductionComplexation of ligands by proteins is the critical process allowing many reactions to occur in the living organisms . Of particular interest is the high specificity of the ligand complexation process . The question of mechanism of mutual recognition is the puzzle specially taking into account large number of proteins and ligands in high concentration in the cell and other solutions in the organism. The information should not only be recognizable in close contact of two interacting molecules. The information should be recognizable even in certain distance not only on the surface of the protein. The immanent presence of water conditioning any living processes is the main candidate to be the messenger in the ligand-protein recognition. The phenomenon of hydrophobic interaction seems to be the key method to distribute the specific information in the cell and liquid tissues in the organism.The fuzzy oil drop model assuming the idealized hydrophobic core structure expressed by 3D Gauss function is able to recognize the local discordance between expected (idealized) and really observed hydrophobic core structure in a particular protein . It was shown in many papers that the local discrepancies are highly specific . Local discordance is the source for indicated specific water molecules ordering which may be propagated involving a few layers of water molecules in the close neighborhood of the surface, where this specific ordering is initiated. The final effect of ligand binding may be different from the point of view of hydrophobic core formation. The example shown in this paper reveals the high ordering of the secondary structure as well as ligand (pentapeptide) present in complex support construction of hydrophobic core of higher order.Materials and methodsDataThe protein structure of PDZ domain in complex with pentapeptide (LYS-GLN-THR-SER-VAL) is the object of analysis. The structure is available from PDB (ID 1BE9) .Hydrophobicity scale applied in the model is the one presented in .Fuzzy oil drop modelThis model has been described in many papers. The presentation of the model is limited to the part necessary for interpretation of results shown in this paper.The protein molecule should be localized with its geometric center in the origin of the coordinate system with the longest diameter of the molecule oriented according to one selected axis (say X-axis) and rotated to co-orient the second diagonal (perpendicular to the first one) of the molecule oriented co-axial with the second axis of the coordinate system. For this orientation the 3D Gauss function can be defined to cover (encapsulate) the complete molecule into the ellipsoid of appropriate size expressed by 3D Gauss function parameters which are SigmaX, SigmaY and SigmaZ. The value of 3D Gauss function in any point belonging to ellipsoid is assumed to represent the expected theoretical value of hydrophobicity in selected point.This value is compared with the really observed hydrophobicity which is the effect of inter-residual hydrophobic interaction. This value depends on the inter-residual distance and on the intrinsic hydrophobicity – the attribute of each amino acid. Any hydrophobicity scale can be applied for this calculation . One should mention that the position of so-called “effective atoms” (atoms representing the whole residue – averaged position of all atoms belonging to residue) is taken for this calculation.Two distributions are obtained according to the described calculations: T – theoretical one – high order with highest hydrophobicity concentration in the center of the molecule and decrease of this value according to increase of distance reaching values of zero level on the surface of protein (in the distance 3*Sigma in any direction) and O – observed one which expresses the real hydrophobicity distribution as the result of inter-residual interaction. These two distributions are not necessarily accordant. The proteins of high accordance have been identified (for example, titin 1TIT). Proteins of high discordance (human protein disulfide isomerase – 1MEK)  where the stability is supported by the presence of one or more disulphide bonds. Many proteins are identified as locally discordant. This local discordance is usually related to the biological function of the protein under consideration. Ligand binding cavity is recognized as the local hydrophobicity deficiency; the area for protein-protein interaction appears to represent local hydrophobicity excess [8, 9].To express the differences in a quantitative way, the Kullback-Leibler divergence entropy  has been introduced to measure the difference between T and O distributions. Since, however, this factor is of entropy character, its value cannot be interpreted as it is. This is why the second reference distribution has been introduced, which represents the status deprived of any form of hydrophobicity differentiation. The reference distribution is of unified form – constant one (R) – representing the status of no hydrophobic core at all. Two values O/T and O/R treat T distribution in first one and R distribution in the second as target. The comparison of these two values gives information about the distance between O distribution and the one of target distribution to be lower. To avoid dealing with two parameters, the RD – relative distance scale – has been introduced. It expresses the O/T distance divided by the sum of O/T and O/R distances. In consequence the RD value <0.5 identifies the status of hydrophobic core as the ordered one, RD>0.5, identifies the closeness of O distribution versus R distribution.The parameters O/T, O/R and RD may be also calculated for polypeptide chain fragments to recognize their local status versus the structure of the hydrophobic core as it appears in a particular molecule.The detailed description of the model is given in .ResultsCharacteristics of the hydrophobic core structure in PDZ domain is given in Table 1.Table 1:Status of fragments (secondary structure) as it appears in 1BE9; the Beta-sheets.Secondary unitFragmentRDComplexChain AComplete unit0.5580.586312–318384–392356–363365–367Sheet I0.5890.597Pentapeptide335–342324–330371–381Sheet II0.4060.492403–407411–415Sheet III0.6350.641The status of complex is expressed by RD=0.558. It means that the structure of the hydrophobic core is not accordant with the expected one. The status of the hydrophobic core of PDZ domain in the absence of pentapeptide is RD=0.586. The discordance of apo-domain appears higher than in complex. It may be interpreted that the pentapeptide which fits very well to Beta-sheet present in protein molecule supports the structure of the hydrophobic core. Taking into account that residues engaged in complexation may be stressed to adopt the position which is the consensus between optimal orientation in respect to the molecular hydrophobic core and interaction with ligand (pentapeptide), the RD was calculated for the part of the domain with residues engaged in ligand complexation eliminated. The RD value for the part of the domain not engaged in ligand binding is equal to 0.587. The differences are small; however, the tendency is increasing suggesting that the ligand plays the stabilizing role for hydrophobic core formation.The profiles T and O shown in Figure 1 visualize the presence of polypeptide chain fragments which are evidently discordant in respect to the expected one. These fragments are distinguished in Figure 1 by black boxes. The elimination of these fragments from RD calculation makes the status of the rest of the molecule accordant versus the expected one. The status of the part of domain is expressed by RD=0.489. It means that this part is responsible for domain stabilization taking the hydrophobic core of ordered form as an attribute of domain stabilization.Figure 1:Theoretical (T) and observed (O) hydrophobicity distribution in PDZ domain.Yellow/blue lines distinguish fragments of high discordance between two distributions shown also shown as black boxes. Black thick line on X-axis – residues engaged in ligand binding.The profiles shown in Figure 1 may be interpreted as follows: fragment 305–318 as well as fragment 322–345 and 362 to C-terminal residue seem to represent the O distribution close to T distribution. However, the fragments distinguished by black boxes around residue 321 and the box between 341 and 351 reveal the presence of higher hydrophobicity than expected. Taking into account low values of T hydrophobicity, one may speculate that these two fragments are exposed toward the environment. The status of the fragment – box between 351 and 361 – visualizes the opposite status showing much lower O hydrophobicity than T hydrophobity. This is interpreted as the presence of cavity. Analysis of 3D structure (Figure 2) supports this interpretation of hydrophobicity profiles.Figure 2:Three-dimensional presentation of PDZ domain with ligand (white) and fragments discordant versus the expected ordered hydrophobic core (red and yellow).The RD values given in Table 1 show that the pentapeptide plays a significant role in stabilization of Beta-sheet II. Beta-sheet II in chain A (ligand absent) is described by RD value close to 0.5 significantly higher in comparison with the status of Beta-sheet II with the pentapeptide present.The role of fragments discordant in respect with the T one may be identified analyzing the presentation of the 3D structure in Figure 2. Fragment 351–358 (yellow one) represents much lower level of hydrophobicity than expected. This is due to the large cavity as can be seen in Figure 2. The two distinguished in red fragments (Figure 2) represent the status of higher hydrophobicity than expected. These two fragments are exposed toward the water environment. On profiles (Figure 1) low hydrophobicity is expected in this area. Such characteristics may influence significantly the water molecules in the neighborhood.The fragments distinguished as red (Figure 2) and shown in Figure 1 are ready to accept the presence of another molecule also with exposed hydrophobic area on the surface. Contact of two areas with high hydrophobicity exposed to water environment is optimal in lowering enthalpic effects.The PDZ domain as participating in many cell junction-associated proteins is probably engaged in complexation of other proteins. The presence of peptide makes the molecule more stable from the point of view of hydrophobic core-based stability. However, local discordances suggest preparedness for further interaction with proteins or other ligands.ConclusionsCommunication between molecules in living organisms seems to play a critical role in maintaining the whole system in action. The communication systems are constructed on the basis of hormone transport  for long-distance communication and for highly important processes which must be under control protecting them against random activation. The short distance communication – as it is suggested based on fuzzy oil drop model analysis – may be mediated by specific water molecule structuralization. The structure of liquid water in standard condition is not known [12, 13]. However, in contact with hydrophobic surface the levitation effect is observed . On the other hand, the charge-charge interaction seems to play the role of ordering water molecules in form depending on the charge distribution, which can be of highly specific form. The dramatic change may be assumed in water molecules ordering according to the change of the character of the contact surface. This model was applied to the explanation of the activity of antifreeze proteins, where the different forms of hydrophobicity exposure on the surface may affect the behavior of water including ordering of water molecules differently than in ice .The presented example is the next one in the set of proteins where the biological activity on molecular level seems to be strongly related to the hydrophobic core structure as it is interpreted using fuzzy oil drop model. The example shows the important role of hydrophobic core structure. Fuzzy oil drop model is able to assess its status in a quantitative way that makes the changes of the molecular status more elucidated.Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.Research funding: The work presented in this paper was financially supported by Jagiellonian University – Medical College grant system: Funder Id: 10.13039/100009045, #K/ZDS/006363 and #K/ZDS/006366.Employment or leadership: None declared.Honorarium: None declared.Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication.References1.Roche O, Kiyama R, Brooks CL 3rd. Ligand-protein database: linking protein-ligand complex structures to binding data. 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Bio-Algorithms and Med-Systems – de Gruyter
Published: Dec 20, 2017
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