STRUCTURAL ROLE OF HYDROPHOBIC CORE IN PROTEINS – SELECTED [605210]

Journal of Proteomics & Bioinformatics
STRUCTURAL ROLE OF HYDROPHOBIC CORE IN PROTEINS – SELECTED
EXAMPLES
–Manuscript Draft–

Manuscript Number: JPB-16-55
Full Title: STRUCTURAL ROLE OF HYDROPHOBIC CORE IN PROTEINS – SELECTED
EXAMPLES
Short Title:
Article Type: Conference Proceedings
Section/Category: Protein Basic Science
Keywords: structure comparison; structure alignment; structural differences; structure prediction;
evolution; protein folding; hydrophobicity
Abstract: This paper discusses the sequence/structure relation. The core question concerns the
degree to which similar sequences produce similar structures and vice versa. A
mechanism by which similar sequences may result in dissimilar structures is proposed,
based on the fuzzy oil drop model in which structural similarity is estimated by
analyzing the protein's hydrophobic core. We show that local changes in amino acid
sequences, in addition to producing local structural alterations at the substitution site,
may also change the shape of the hydrophobic core, significantly affecting the overall
tertiary conformation of the protein. Our analysis focuses on four sets of proteins: 1.
pair of designer proteins with specially prepared sequences, 2. pair of natural proteins
modified (mutated) to converge to a point of high-level sequence identity while
retaining their respective wild-type tertiary folds, 3. pair of natural proteins with
common ancestry but with differing structures and biological profiles shaped by
divergent evolution and 4. pair of natural proteins of high structural similarity with no
sequence similarity and different biological function.
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STRUCTURAL ROLE OF HYDROPHOBIC CORE IN PROTEINS – SELECTED
EXAMPLES

Mateusz Banach, 1,2 Barbara Kalinowska, 1,2 Leszek Konieczny,3 Irena Roterman1*

1Department of Bioinformatics and Telemedicine – Jagiellonian University – Medical College,
Łazarza 16, 31-530 Krakow, Poland
2Faculty of Physics, Astronomy and Applied Co mputer Science, Jagiellonian University,
Łojasiewicza 8, 30-348 Krakow, Poland
3 Chair of Medical Biochemistry, Jagiellonian University – Medical College, Kopernika 7, 31-
034 Krakow, Poland
Correspondence to : Irena Roterman, Department of Bioinformatics and Telemedicine,
Łazarza 16, 31-530 Krakow, Poland. E-mail: [anonimizat]
Keywords: hydrophobicity, structural similarity, homology, tertiary structure, sequence-to-
structure relation

Abstract:

This paper discusses the sequenc e/structure relation. The core que stion concerns the degree to
which similar sequences produce similar struct ures and vice versa. A mechanism by which
similar sequences may result in dissimilar struct ures is proposed, based on the fuzzy oil drop
model in which structural similarity is estimated by analyzing the protein’s hydrophobic core. We show that local changes in amino acid sequen ces, in addition to producing local structural
alterations at the substitution site, may al so change the shape of the hydrophobic core,
significantly affecting the overall tertiary conformation of the protein. Our analysis focuses on
four sets of proteins: 1. pair of designer proteins with specially prepared sequences, 2. pair of
natural proteins modified (mutated) to conve rge to a point of high- level sequence identity
while retaining their respective wild-type tertiary folds, 3. pair of natural proteins with
common ancestry but with differing structures a nd biological profiles shaped by divergent
evolution and 4. pair of natural proteins of high structural simila rity with no sequence
similarity and differe nt biological function.
Keywords : structure comparison; structure alignm ent; structural differences; structure
prediction; evolution; protein folding; hydrophobicity
Introduction

The presented analysis concer ns the well known problem of co rrelating the protein’s amino
acid sequence with its 3D structure [1-4]. The search for algorithms which can be used to
translate the former into the latter is a funda mental problem in prot eomics [5,6] and often
yields useful insight into the specific properties of individual proteins [7].
A classic example of this phenomenon is th e group of structures referred to as
immunoglobulin-like domains. Such domains are present in all immunoglobulins (where they
determine their function) but are also encounter ed in enzymes and tran sport proteins [8-10].
Immunoglobulins exhibit high stru ctural similarity, adopting characteristic “sandwich”
conformations with ra ther low sequence similarity. Even among immunoglobulins domains Manuscript
Click here to download Manuscript SB16_Manuscript_Irena
Roterman1.pdf

the λ and κ sequences are identified. Of course, th e diversity of proteins which are not
immunoglobulins but which do contain immunoglobu lin-like domains is even greater [10].
In addition to the above, studies have reveal ed cases where very similar sequences produce
significantly different structural forms [11]. For example, the KGVVPQLVK sequence
generates a classic β-twist in 1PKY but adopts a helical conformation in 1IAL [12-14]. The
three 7-residue sequences which also share this property of different secondary structure for
identical sequences are given in [15]. Conservative hydropathic identity at geometrically equivalent positions is the object of
analysis in [16]. Our work focuse s on structural differences in four pairs of proteins: 1. pair of
designer proteins with specially prepared sequ ences, 2. pair of natu ral proteins modified
(mutated) to converge to a point of high-le vel sequence identity while retaining their
respective wild-type tertiary folds, 3. pair of natural proteins with common ancestry but with
differing structures and biologi cal profiles shaped by divergent evolution and 4. pair of
natural proteins of high stru ctural similarity with no seque nce similarity and different
biological function. In attempting to show the role of hydrophobic core structure in structural stabilization we
refer to the fuzzy oil drop model, which predic ts the 3D conformation of the target protein by
simulating the emergence of a hydrophobic core. While our research has identified some
interesting correlations, generalizing them re mains an open issue: in order to determine
whether the presented results may, in fact, be ge neralized we need to process a much larger
database of proteins.
Materials and methods
Data
The presented analysis concerns four sets of tw o proteins each. The first set comprises two de
novo designed proteins with a se quential similarity of 88% but with differing 3D structures.
The second describes two natural proteins which are modified (m utated) in a stepwise fashion
in order to align their sequences while preser ving structural different iation (helix-to-Beta).
The third set includes two natural homologues with common ancestry. The fourth one
discusses pair of natura l proteins of high structural simila rity with no sequence similarity and
different biological function.
De novo design
Two de novo designed proteins, 2JWU and 2JWS, also referred to as G
A88 and G B88 share
88% sequence identity but different folds [17] . The geometries of th e seven nonidentical
residues (of 56 total) provide insight into th e structural basis for switching between 3- α and
α/β conformations. Further mutation of a subs et of these nonidentities, guided by the G A88
and G B88 structures, leads to proteins with even higher levels of sequence identity (95%) and
differing folds. Thus, conformational switchi ng to an alternative monomeric fold of
comparable stability can be effected with just a handful of mutations in a small protein. This
result has implications for understanding not only the folding code but also the evolution of
new folds. The CATH [18] classification fo r these two proteins is as follows: 1.10.8.40 –
Mainly Alpha Orthogonal Bundle for 2JWS and 3.10.20.10. – R-Alpha Beta Roll for 2JWU.

Wild type proteins with aim-oriented mutations
Two proteins: G311 (1ZXG) and A219 (1ZXH) are modified versions of wild-type proteins
designated G and A (IgG binding domains, source: Staphylococcus aureus for 1ZXG and
Streptococcus sp for 1ZXH) respectively [19]. The series of mutations aimed at achieving a
high level of sequence identity while preserving wild-type 3D structures. Both proteins (G311

vs. G and A219 vs. A) represent backbone RM S-D 1.4Å, maintaining wild-type secondary
structures: α/β for G311 and helical for A219. The fi nal sequence identity of both modified
proteins is on the level of 59%. All releva nt data was taken fr om a paper describing
experimental results of pr otein modifications [19].

Homologous proteins
The next pair comprises two proteins with co mmon ancestry but different folds and functions:
2PIJ (Pfl 6 BETA) (source: Pseudomonas fluorescens) Cro protein from prophage pfl 6 in P.
fluorescens pf-5 [20] and 3BD1 (Xfaso 1) Cro pr otein from putative prophage element X.
fastidiosa strain ann-1 [20] (source: Xylella fastidiosa ). Both proteins share an identical
CATH classification: 1.10.260.40 – Mainly Alpha Orthogonal Bundle.
The differences between homologous proteins are due to evolutionary pressure. In the
presented case the sequence identity is 40%, yet the α-helix is replaced by a β-sheet in the C-
terminal region spanning approximately 25 re sidues. According to [20], sedimentation
analysis suggests a correlation between helix-t o-sheet conversion, along with strengthened
dimerization.
Unrelated proteins of similar fold
Two proteins not related in respect neither to evolution nor to function representing however
the common fold classified by CATH as 3.40.50.360 – 3CHY (signal tr ansduction protein)
[21] and 3.40.50.2300 – 1RCF (flavodoxin) [22] both of 3-layer (aba) sandwich form with no
sequence similarity (about 19%).
Introduction to the fuzzy oil drop model
The fuzzy oil drop (FOD) model is a modificati on of the previously described oil drop model
which asserts that hydrophobic residues tend to mi grate to the center of the protein body while
hydrophilic residues are exposed on its surface [23,24]. A visual description of this model is presented in Fig. 1.A where the dark area corresponds to a highly hydrophobic “core” while
light areas represent the hydrophili c “shell”. The fuzzy oil drop replaces the bina ry discrete
model [25] with a continuous function peaking at the center of the molecule [23], which
causes hydrophobicity density values to decreas e along with distance from the center,
reaching zero on the molecular surface. Visu al comparison between the two models is
presented on Fig. 1.B. The appropriate hydrophobici ty distributions are shown in Fig. 1C and
Fig.1.D respectively.

Fig. 1. Comparison between the classi cal discrete oil dr op model (A and C) and the fuzzy oil
drop model (B and D). Circles represent posi tions of intrinsically hydrophobic (dark) and
hydrophilic (white) residues. The charts repres ent the assumed distri bution of hydrophobicity
density in each model, where hydr ophobic residues are lo cated near the center of the molecule
and hydrophilic on its surface.
The above-mentioned continuous hydrophobicity de nsity distribution can be represented by a
3D Gaussian function, which assumes the shap e of a bell curve centered on the mid-range
point of the free variable distribution range. Accordingly, the mol ecule is encapsulated in an
axis-aligned ellipsoid upon which this 3D Gaussi an function can be superimposed. The size of
this ellipsoid (expressed by three sigma parame ters) corresponds to the approximate size of
the protein under consideration. The idealized hydrophobicity di stribution in protein body
follows the 3D Gauss function:
() ()()
⎟⎟
⎠⎞
⎜⎜
⎝⎛− −
⎟⎟
⎠⎞
⎜⎜
⎝⎛− −
⎟⎟
⎠⎞
⎜⎜
⎝⎛− −=22
22
22
2exp2exp2exp1
zj
yj
xj
sumjz z y y x x
HtHtσ σ σ

,

jHtis the theoretical hydrophobi city density (hence the t designation) at the jth point in the
protein body. The zyx,,
z y x correspond to the peak of the Gaussian in each of the three principal
directions, while σσσ,, denote the range of arguments fo r each coordinate system axis.
These coefficients are selected in such a way that 99% of the Gaussian’s integral is confined
to a range of σ3±x . Values of the distribution can be assumed to equal 0 beyond this range.
If the molecule is placed inside a cap sule whose dimensions are given by
z y x z y xσσσ 3±
z y x, 3 , 3± ± then the values calculated for ar bitrary point of the corresponding
Gaussian represent the idealized hydrophobicity de nsity distribution for th e target protein. If
σσσ= = , the capsule is perfectly s pherical; otherwise it is an ellipsoid. The Gaussian
yields hydrophobicity density valu es at arbitrary points in the protein body – for example at
points which correspond to the placement of effective atoms (averaged position of atoms
belonging to particular amino acid). is the hydrophobicity density determined for the j-th
amino acid while x, y and z indicate the placement of its corresponding effective atom. jHt
The denominator of
sumHt1
jHt
jHt expresses the aggregate sum of all values given by the Gaussian
for each amino acid making up the protein. This enables normalization of the distribution
since will always be equal to 1.
values reflect the expected hydrophobicity density which should correspond to each
amino acid in order for the hydrophobic core to match theoretical predictions with perfect
accuracy (with all hydrophobic residues interna lized and all hydrophilic residues exposed on
the surface). The closer to the surface the lower the e xpected hydrophobicity density.
The position of the j-th residue is represented by so calle d “effective atom” which is localized
at the geometric center of each residue (averaged position of all atoms belonging to the
particular amino acid).
The picture Fig.2.A. visualizes also the method to express the size of protein molecule in σ-
units. Fig.2.B visualizes the encapsulation of protein molecule in gradually changed hydrophobicity (from low-green on the surface to high – red in the center)

Fig 2. Graphical representation of the encapsulati on of the protein molecule with a 3D
Gaussian. A – one-dimensional Gaussians plotted along the horizontal and vertical axes. The volume of
the capsule (drop) is determined by σ coefficients. Since σ
x> σy, the molecule is stretched
along the X axis. The boundary of the capsule is given by the so-called three-sigma rule (X±3σ
x, Y±3σ y, Z±3σz).

B – protein molecule encapsulated in an ellipso id. Changes in coloring (from gray to purple)
represent the varying hy drophobicity density of effective at oms (density decreases along with
distance from the center of the capsule).
On the other hand the actual di stribution of hydrophobicity density observed in a protein
molecule depends on inter-chain interactions , which, in turn, depend on the intrinsic
hydrophobicity of each amino aci d. Intrinsic hydrophobicity can be determined by
experimental studies or theoretical reasoning – our work bases on the scale published in [24]
while the force of hydrophobic interactions has b een calculated using other scales as it was
shown in [24]. For each amino acid j (or, more accurately, for each effective atom) the sum of
interactions with its neighbors is computed and subsequently normalized by dividing it by the
number of elementary interactions (f ollowing the function proposed in [26]:

∑
=
⎪⎪
⎩⎪⎪
⎨⎧
>⎥⎥
⎦⎤
⎢⎢
⎣⎡
⎟⎟
⎠⎞
⎜⎜
⎝⎛
⎟⎟
⎠⎞
⎜⎜
⎝⎛−⎟⎟
⎠⎞
⎜⎜
⎝⎛+⎟⎟
⎠⎞
⎜⎜
⎝⎛−⎟⎟
⎠⎞
⎜⎜
⎝⎛−
+ =N
i
ijij ij ij ij
r
jr
i
sumj
c rcr
cr
cr
cr
H HHoHo
18 6 4 2
for 0for 5 9 7211
) (1 ≤ijc r
r
iHr
jH
sumHo
N is the number of amino acids in the protein, and expresses the hydrophobicity
parameter of the i-th and j -th residues while rij expresses the distance between two interacting
residues ( j-th effective atom and i-th effective atom). The parameter c expresses the cutoff
distance for hydrophobic interactions, which is taken as 9.0Å (following [26]). The
coefficient, representing the aggregate sum of all components, is n eeded to normalize the
distribution which, in turn, enables meaningful comparisons between the observed and
theoretical hydrophobicity density distributions. The residues in the protein body may be locat ed properly – hydrophobic in the center and
hydrophilic on the surface. However they may not follow this rule (Fig.3.A and Fig.3.B). The
discrete model can be used to qualitatively char acterize each residue as either “properly” or
“improperly” located in the pr otein body (Fig. 3.C). In contra st, the continuous (fuzzy oil
drop) model expresses this phenomenon in quan titative terms (Fig. 3. D). If we assign two
parameters to each residue – its theoretical (T) and observed (O) hydrophobicity density – and
then present both values for all residues in the protein chain in the form of a profile chart, the resulting charts can be superimposed to di scover areas of agreement/disagreement between
both distributions.

Fig 3. Hydrophobicity density distribution according to the discrete and continuous m odel.
Here, the placem ent of residues m ay not co rrespond to th eir in trinsic hydrophobicity. For
exam ple, som e white c ircles (hyd rophilic re sidues) a re loc alized in the central part of the
protein body (left). The right-hand diagram presents the continuous distribution, with shades
of grey indicating hydrophobicity. Two diagra ms present the hydrophobicity distribution: T
(blue) – expected and O (red) observed for discrete (left) and continuous model (right).
The Fig 1. and Fig 3. intentionally resem bles the one presented in [27] so as to visu alize the
continuity and evolution of theoretical hydrophobic core m odels.

The two diagram s are accom panied by hydrophobicity density distribution pro files: the
expected (T) and observed (O) distribution. The la tter of these takes in to account the variable
intrinsic hydrophobicity of each re sidue, and its location in the protein body (which does no t
necessarily correspond to its individual properties).
Quantita tive analys is, ex pressing the differences between th e expected ( T) and obse rved (O )
distribution, is based on Kullback-Lei bler divergence entropy for mula [28]:
0
2
10/(log ) (i iN
ii KL pp p pp D∑
==Ι

The value of DKL expresses the distance between the observed ( p) and target ( p0) distributions,
the latter of which is given by the 3D Gaussian (T). The observed distribution ( p) is referred
to as O.
For the sake of simplicity, we introduce the following notation:
) / (2 i iT O log
1N
iiO T O∑
==
Since DKL is a measure of entropy it must be compar ed to a reference value. In order to
facilitate meaningful comparisons, we have introduced another opposite boundary distribution
(referred to as “uniform” or R) which corres ponds to a situation where each effective atom
possesses the same hydrophobicity density (1/ N, where N is the number of residues in the
chain). This distribution is depr ived of any form of hydrophobici ty concentration at any point
in the protein body:
) /i iR ( log
12N
ii O O R O∑
==
Comparing O|T and O|R tells us whether the gi ven protein (O) more closely approximates the
theoretical (T) or uniform (R) distribution. Proteins for whic h O|T > O|R are regarded as
lacking a prominent hydrophobic core. To furt her simplify matters we introduced the
following relative distance (RD) criterion:

RD = O│T / (O│T + O│R)

RD < 0.5 is understood to indicate the pres ence of a hydrophobic core. Fig. 4. presents a
graphical representation of RD values, restricted (for simplicity) to a single dimension.
D
KL (as well as O|T, O|R and RD) may be calcu lated for specific structural units (protein
complex, single molecule, single chain, selected domain etc.) In such cases the bounding ellipsoid is restricted to the selected fragment of the protein. It is also possible to determine the status of polypeptide chain fragments with in the context of a given ellipsoid. This
procedure requires prior normalization of O|T and O|R values descri bing the analyzed
fragment.

Fig 4. Graphical representation of fuzzy oil drop model hydrophobicity dist ributions obtained
for a hypothetical protein reduced to a single di mension for simplicity. A – theorized Gaussian
distribution (blue) while the chart C corresponds to the uniform distribu tion (green). Actually
observed (red) hydrophobicity density distribu tion in the target protein B, while its
corresponding value of RD (relative distance), in D is marked on the hori zontal axis with a
red diamond. According to the fuzzy oil drop model this protein doe s not contai n a well-
defined hydrophobic core, because its RD value, equa l to 0.619, is above the 0.5 threshold (or
– generally – closer to R than T).

RD values calculated for a selected fragment (following normalization of T
i and O i values of
the fragment under consideration) calculated for the example given in Fig. 3.D. are as follows: the complete profile in Fig. 3.D corresponds to RD = 0.613; however th e fragment at 2-5 is
characterized by RD = 0.283. The interpretation of this distribution is that, as a whole, the
molecule lacks a stable hydrophobi c core, although the selected fragment (2-5) represents
very good local agreement between the obser ved and idealized hy drophobicity density
distribution. The status of 2-5 fragment can be interpreted as responsible for local hydrophobic core stabilization inde pendently on the status of complete distribution as
discordant versus the T distribution.
The above procedure will be appl ied in the analysis of proteins described in this paper. By
restricting our analysis to i ndividual fragments, we can determine whether a given fragment
participates in the formation of a hydrophobic core. In particular, fragments of chain
representing well defined seconda ry folds which satisfy RD < 0. 5 are thought to contribute to
structural stabilization, while fragments for which RD >= 0.5 are less stable. Such fragments,
if present on the surface of the protein, may potentially form complexation sites. The
fragments of chains are defined by their seco ndary structure. Identif ication of secondary
structural folds and the compos ition of protein domains follows the CATH [18] and PDBsum
[29] classifications. Likewise, inter-domain/inte r-chain contacts have been identified on the
basis of the PDBsum di stance criteria [29].
The OORF system of RD calculation uses the method from ORF calculation in DNA analysis.
OORF stands from Overlapped Open Reading Fram e. The window of declared size (10 aa in
our analysis) is taken as the fragment, the RD value is calculated. For example fragment 1-10
gets described by its RD value. Then the next window (2-11 aa) is taken for RD calculation.
The RD value for each window requires prior normalization (the sum of T
i and O i belonging
to the window shall be equal to 1.0). This fo rm of calculation makes possible characteristics
of entire chain regardless the secondary structure.

Results
De novo designed proteins
According to results given in Ta b. 1. the structure of 2JWS (G A88) is consistent with the
model both as a whole and in its packed secti on (without the N-terminal fragment 1-7 which
was eliminated from calculation since the fuzzy oil drop model wo rks well with globular
proteins). This operation does not aff ect the status of helical folds.
In 2JWU (G B88) four β -folds can be distinguished, in additi on to a single helix. This molecule
also contains a loop (38-41). The β-fragment at 42-46 and the loop both diverge from the
model even though in G A88 the same residues form parts of an accordant helix. The fragment
at 38-46 is characterized by higher-than-expected hydrophobicity density (Fig. 5.A). Since

this fragment is exposed on the protein surf ace (expected hydrophobicity is low), it may be
responsible for possible forming complexes with other proteins which also expose
hydrophobic areas on their surface.
The consistently high accordance of 2JWS – both as a whole a nd when subdivided into folds
– suggest a relative lack of local deformations. It may be speculated that as predicted by the
fuzzy oil drop model, this molecule is highly wate r-soluble with low tendency to interact with
any ligand molecule.
Table 1.
Properties of selected proteins from the point of view of the fuzzy oil drop model.
O|T values indicate the distance between the obs erved and theoretical distribution while O|R
values show the corre sponding distance between the observed and uniform distribution. RD
values are in relation to the idealized (theoretical) distribution. Each parameter is listed for
complete molecules and for their individual folds. The leftmost column also includes
information on sequential discrepancies between pairs of molecules. Mut – N indicates an
exchange and the number of affected resi dues (2JWS vs. 2JWU) in each fragment. The
bottom part of the table shows results for the packed domain of 2JWS (without the
unstructured N-terminal fragment). B stands for β-type structures while H indicates a right-
handed α-helix.
SECONDARY FRAGMENT O|T O|R RD
2JWU(G B88) COMPLETE
MOLECULE 0.126 0.249 0.335
B 1-9 0.052 0.157 0.249
B 12-20 0.196 0.248 0.441
Mut – 4 H 22-37 0.146 0.203 0.419
L 38-41 0.078 0.069 0.533
Mut – 1 B 42-46 0.203 0.160 0.558
Mut – 1 B 50-56 0.066 0.180 0.268

2JWS(G A88) COMPLETE
MOLECULE 0.182 0.308 0.371
Unstructur. 1-7 0.235 0.241 0.493
Mut – 1 H 8-24 0.260 0.322 0.447
Mut – 2 H 26-35 0.055 0.251 0.181
Mut – 3 H 38-52 0.129 0.179 0.418

2JWS (G A88)
8-56 COMPLETE DOMAIN 0.170 0.277 0.380
Mut – 1 H 8-24 0.213 0.328 0.394
Mut – 2 H 26-35 0.078 0.250 0.238
Mut – 3 H 38-52 0.161 0.175 0.479
Fig 5. A and Fig 5 D present the hydrophobicity density profile s for both proteins, showing
the values ascribed to each residue in the polypeptide chain. The distinguished fragments satisfy the condition of high expected and high observed hydrophobicity in both molecules.
From the point of view of the model both molecules contain well-defined hydrophobic cores.
One shall notice that the fuzzy oil drop model iden tifies the central part of molecule as the
hydrophobic core together with the shell of interm ediate coat including the exposed surface of
expected hydrophobicity close to zero (hydrophilic surface). The co-existence of these two

parts makes the hydrophobic core complete as protected and isolated against immediate
contact with water environmen t. The identification of resi dues recognized as hydrophobic
core members is based on the high expect ed and high observed hydrophobicity. Residues
following this condition are recognized as re sponsible for hydrophobic core construction.
The profiles shown in Fig 5.B and Fig 5.C. (OORF distributions) reveal significant
differences pointing different fragments of low RD values suggesting high accordance
between expected and observed di stributions in both proteins.

Fig 5. Hydrophobicity density distribution profiles for two molecules ( de novo design)
differing with respect to their seco ndary structure: A, B – 2JWS (G A88), C, D – 2JWU
(GB88). Theoretical hydrophobicity profile is plotted in blue while that of observed
hydrophobicity is red. Vertical green lines loca lize positions of muta tions. Orange shades
under the profiles indicate pos itions of hydrophobic core, unders tood as groups of residues

with peak values of both hydrophobicity distribu tions. Figures 5.B and 5.C present RD values
of both proteins calculated in the OORF (Overl apped Open Reading Frame) system with 10
aa window size. Red and yellow fragments visi ble on those figures denote locations of
secondary structure fragments: α -helices and β-sheets, respectively.

The observations listed above seem to sup port the conclusion that both proteins are
structurally different in terms of their hydrophobic cores. The construction of hydrophobic
core in 2JWS is generated by central part of polypeptide chai n, comprising two fragments
(Fig 5.A) while in 2JWU, it requires three separa te fragments to participate in core generation
(Fig 5.D). At this point it might be interesting to speculate about the progress of the folding process in
each of these two cases. In 2JWS the hydrophobic co re nucleates near the center of the chain,
with the remaining sections aligning themselves to the emerging core. While in 2JWU the nucleation is mainly constructed by N- and C-terminal fragments with the participation also of central fragment of the chain. Figure 6 presents a comparison of the status of each fold in both proteins, indicating
mutations and the correspondence between th e observed and theore tical hydrophobicity
density in each fold. The makeup of the hydrophobic core is also depicted.

Fig 6. 3-D protein structure m odel. A – 2J WU, B – 2J WS.
Colors indicate the s tatus of each fragm ent: re d area diverges from the model while b lue ones
remain consisten t with it. Y ellow fragments m ark the loc i of mutations.
In summ ary, the introduction of seven m utations (G24A, I25T, I30F, I33Y, L45Y, I49T,
L50K – with 2JWS serving as the reference stra in) resu lts in a f ar higher conc entration o f
hydrophobic residues in 2JW S. Thi s enlarges th e hydrophobic core w hich is formed by the
central frag ment of the polypeptid e chain. Unlike 2 JWS, in 2JW U the core is made up of
three separate fragm ents, including one th at form s part of the shell (w ith lower
hydrophobic ity dens ity). Substitu tions at G42A , I25T, I30F, I33Y, L45Y result in the
appearance of a long fra gment which for ms part of the hydrophobic core, while the presence

of Y, T and K in the C-terminal fragment of 2JWU causes a hydrophobic ity density gradient
to emerge in the surface zone where hydrophilic residues appear, in accordance with the
theoretical model. Fig 5. shows clearly the in fluence of mutations si nce the residues changed
concern the positions of the central part in 2J WU. The location of these residues in 2JWU is
rather distributed. In consequence different fragments of the chain participate in hydrophobic core formation and one fragment (the β-structural fragment) appears to represent the
hydrophobicity density distribution discor dant versus the idealized one.

Wild type proteins with aim-oriented mutations

The results listed in Table 2. indicate very high agreement with the fuzzy oil drop model in
two compared proteins: 1ZXH and 1ZXG – two IgG binding domains. Additionally, each
secondary structure (including loops) remains cons istent with structural predictions provided
by the model.
Table 2. Properties of selected proteins from the point of view of the fuzzy oil drop model.
O|T values indicate the distance between the obs erved and theoretical distribution while O|R
values show the corre sponding distance between the observed and uniform distribution. RD
values are in relation to the idealized (theoretical) distribution. Each parameter is listed for
complete molecules and for their individual folds. The leftmost column also includes
information on sequential discrepancie s between pairs of molecules. Mut – N indicates an
exchange and the number of affect ed residues in each fragment.
SECONDARY
FRAGMENT O|T O|R RD
A219 (1ZXH) COMPLETE
MOLECULE 0.085 0.189 0.310
Mut 1 B 1-9 0.111 0.124 0.471
Mut 4 B 12-20 0.059 0.134 0.305
Mut 6 H 22-39 0.079 0.173 0.313
Mut 3 B 42-44 0.101 0.279 0.266
Mut 4 L 45-49 0.067 0.073 0.478
Mut 3 B 50-53 0.255 0.180 0.056
B 54-55 0.039 0.160 0.197

G311 (1ZXG) COMPLETE
MOLECULE 0.095 0.288 0.248
L 1-7 0.087 0.196 0.308
Mut 2 H 8-18 0.079 0.308 0.205
Mut 5 L 19-24 0.039 0.177 0.183
Mut 2 H 25-37 0.070 0.262 0.211
Mut 11 H 40-55 0.069 0.218 0.242
L 56-59 0.100 0.493 0.168
Considering the large set of molecules anal yzed using the fuzzy oil drop model we can
conclude that the presented proteins are among the most accordant in the entire set, as indicated by their RD values (so far RD = 0.38 for the immunoglobulin -like domain in titin
(1TIT) was found to be the lowest). The structure of the hydroph obic core, which is
understood as the entire tertiary conformation of the protein (including th e core itself and its

hydrophilic sheath) remains highly consistent with theoretical predictions, as shown in Figs.
7.A and 7.B. Figs. 7.C and 7.D illustrate th e agreement between theoretical and observed
hydrophobicity density distributi ons, with correlation coeffici ents of 0.847 and 0.784 for
G311 and A219 respectively. The figures also reveal highly hydrophobic (core) and
hydrophilic (surface) residues, whos e placement can be seen in Fig. 8.A. Finally, Fig. 8.B.
marks the loci of point mutations – though the aff ected residues do not clearly belong either to
the core or to the hydrophilic sheath. Fig 8 vi sualize the positions of mutations and their
influence on the hydrophobic core rearrangement.

Fig 7. Hydrophobicity density distributions and rela tions between them: A, B – G311, C, D –
A219. Red, pointing upwards triangles mark re sidues accordant with the model and exhibiting
high values of both kinds of hydrophobicity. Blue, pointing downwards triangles present
denote residues also accordant with the models, however presenting low hydrophobicity
qualities. Cutoffs of 0.03 and 0.01 were chosen arbitrarily. Both proteins are highly accordant
with the model, which also causes hi gh correlation between their hydrophobicity
distributions: 0.85 a nd 0.78 respectively.

Fig 8. 3D presentation of A219 and G311 molecules with highlighted residues.
A1 – G311 –red – hydrophobic core (as marked in Fig 7.A). B1 – A219 –red – hydrophobic
core (as marked in Fig 7.C) A2 – G311 – orange – residues differing (m utations) from those
in A219. B2 – A219 – orange – residues differing (mutations) from those in G311.

Analysis of results for G311 and A219 indicates that tertiary structural stabilization (by
hydrophobic core) appears to be dependent on a proper distribution of hydrophobicity density,
ensuring the presence of a highly hydrophobic co re as well as the encapsulating hydrophilic

sheath, with near-zero hydrophobicity density va lues on its surface. Unfortunately the authors
of the cited experimental work [17] do not report on the relation between the introduced
mutations and the proteins’ capability to bind immunoglobulins. From the point of view of the
fuzzy oil drop model, however, the mutated molecules should be less prone to complexation than their wild-type counterparts. This suppos ition follows from the observed good agreement
between the theoretica l and observed hydrophobicity dens ity distributions – note that
complexation sites are typically characterized by marked differences between both profiles
(theoretical and observed). Acco rding to the model, a protein which only exposes hydrophilic
residues on its surface should be highly soluble and incapable of inter acting with any ligands
other than dissolved ions. This phenomenon is evidenced by an tifreeze proteins, which exhibit
near-perfect accordance with the theoretical hydr ophobicity density distri bution [30]. The role
of these proteins is to be well soluble wit hout any specific interact ion with any molecules
from environment except water to not allo w the ice-structuralization of water.

Homologous proteins
Two proteins of common an cestry: 2PIJ and 3BD1 are character ised in Tab. 3. Both of them
represent well defined hydrophobic co re (distribution of observed hydrophobi city density is
similar to expected one – RD below 0.5). Two secondary structur al fragments were
recognized as locally discordant in 2PIJ and one in 3BD1.
Table 3. Comparison of fuzzy oil drop paramete rs for homologous proteins. O|T, O|R and RD
values indicate the status of each molecule and each of its secondary structural fragments. “L”
and “P” codes appearing in the leftmost colu mn indicate involvement in ligand binding and
protein complexation respectively. H and B denotes helical and β-structural secondary
fragments respectively.
SECONDARY FRAGMENT O|T O|R RD
2PIJ COMPLETE
MOLECULE 0.118 0.123 0.489
B 2-5 0.088 0.161 0.356
H-6-13 0.023 0.194 0.105
H 15-24 0.077 0.034 0.689
H 26-36 0.036 0.044 0.453
B 39-45 0.105 0.178 0.370
B 49-55 0.077 0.046 0.625
3BD1 COMPLETE
MOLECULE 0.065 0.085 0.433
A
H 2-12 0.042 0.057 0.420
H 13-22 0.025 0.014 0.646
H 24-35 0.030 0.098 0.236
L, P H 38-41 0.035 0.058 0.378
P H 42-49 0.030 0.067 0.309
L H 54-59 0.047 0.070 0.403
L 50-53 0.014 0.091 0.135

Fig 9. Distribution of RD values calculated us ing the OORF system (10 aa Overlapped Open
Reading Frame) for two hom ologous proteins: 2PIJ – A and 3BD1 – B. Red and yellow
fragments denote locations within the sequence of α-helices and β-sheets, respectively.

Analysis of RD values calcu lated using the OORF system for two homologous proteins
reveals differences in the struct ure of their hydrophobic cores. In 3BD1 nearly the entire chain
remains consistent with theoretical predictions (with the exception of several frames in the C-
terminal section of the chain) . The OORF profile visu alize opposite role of certain fragments
of the chain. In 2PIJ the central fragment (20-30 windows) represent local maximum, while
analogical fragment in 3BD1 reaches its lowest level of RD values. In 2PIJ the RD parameter
reaches higher values, especially in the central and the C-terminal fragment of the chain. Both
distributions are characterized by low values fo r the N-terminal fragment (positions 1-10)
where the RD parameter does not generally exceed 0.5. The presence of a complexation partner (marke d “P” in Tab. 3) or a ligand (“L”) does not
seem to affect hydrophobicity dens ity distribution in th e relevant areas. In general, whenever
ligand interaction requires a la rge discordant cavity, the corr esponding deviation can usually
be noted by analyzing the hydroph obicity density distribution pr ofile (which is not the case
here) [30]. Similarly, protein complexation of ten occurs in areas of excess hydrophobicity
exposed on the protein surface – which, again, is not the case with the presented protein [30].
By comparing the results presented in Tab. 3 and Fig. 9, we can conclude that 3BD1
possesses a more stable structure, resembling th e idealized “fuzzy oil drop” (i.e. with limited
differences between the observed and theoretica l hydrophobicity density distributions). Fig.
10. reveals variations in the status of each fold.

Fig 10 . 3-D structure of hom ologous proteins. A – 2PIJ, B – 3BD1.
Colors indicate th e statu s of each fragm ent: re d areas div erge from the model while cyan ones
remain consistent, as shown in Table 3.

Unrelated proteins of common fold
Two proteins: 3CHY wild-type CheY from Esch erichia coli, where re sidue Asp-57 (supported
by Lys-109) undergoes phosphorylation and 1RCF – oxidized recom binant flavodoxin from
the cyanobacterium Anabaena 7120 responsible fo r electron transfer from photosystem I to
ferredoxin-NADP(+) reductase [22].
The distributions of expected and observe d hydrophobicity density distribution in both
prote ins rev eal the h igh similarity betw een th ese two profiles. It is also expressed by low
values of RD: 0.300 (O| T=0.089, O| R=0.207 ) for 1RCF and RD = 0.443 (O |T=1.147,
O|R=0.185) for 3CHY. However the secondary fragm ents representing th e status of RD>0.5
were found. The helical fragm ent (112-128) in 3CHY a ppeared to represent the status
discordant versus the m odel as well as the loop (76-81). Two α-stru ctural fragm ents (48 -54,
120-122) in 1RCF represent the st atus discordant vers us the model as well as the loop 90-98
(Fig.11.).

Fig 11. Profiles of theoretical (b lue) hydrophobicity, observed (re d) hydrophobicity and RD
(black) values in 10-aa OORF system dist ributions: A and B – 1RCF, C and D – 3CHY.
Green shades between/under th e profiles indicate local hydr ophobicity discrepancies.
Meaning of red and yellow fragments is the same as in figures 5 and 9.
The location of fragments re presenting the distribution of hydrophobicity density in 3D
structure of both proteins appeared to be di fferent. The fragments placed rather on the surface
of protein in 3CHY (Fig. 11.C and D and Fig.12.B) represent the discordant status while in
1RCF the dissimilarity versus the model is oc curring in the central part of the molecule
(Fig.11.A and Fig. 11.B). This observation ma y suggest different instability of these two
molecules, assuming that other than regular ordered hydrophobicity density distribution may
influence the local stability. The biological activity of 3CHY requires complexation with

other protein molecule [21]. The discordance identified on the protein surface suggests
potential area ready for complexation as may be concluded from the fuzzy oil drop model.
The local instability (local discordance observa tion versus expectation) in this case implies
substantially different potential tendency to structural differen tiation. The lower stability may
be supposed in 1RCF as the disagreement is lo calized in the core of the molecule makes the
β-structural less stable in comparison to analogical β-structural part in 3CHY . It may suggests
the easier destabilization of en tire molecule (1RCF) while th e stable core in 3CHY may
protect the molecule against decomposition of the central part of the molecule.
One shall note that the diverg ence entropy used to measure th e differences between profiles
recognizes as different positions of opposite te ndency. Even large surface between profile
may be ignored by divergence entropy calculation as long as two profiles represent similar
tendency.

Fig 12. 3D presentation of A – CHY and B – 1RCF
Green space-filling – residues engaged in biological activity (according to [21])
Yellow fragm ents – RD above 0.5 rec ognized according to OORF calculation.
Red fragm ents – disco rdant fragm ents accord ing to RD calculated for seco ndary fragments.
These two proteins not related one to the othe r (sequence sim ilarity of only 19% (Clustal2.1
calculation with standard param eters) show s tha t the structu ral sim ilarity does not necessarily
ensures s imilar s tability of the protein taken the interpretation of fuzzy oil drop m odel as the
criter ia for stability estim ation.

Discussion and conclusions

The study of sequence-to-structure correlations in proteins has a long history [31]. This work hints at the im portance of the hydrophobic core in determ ining the protein’s tertiary
confor mation. Our observations support the sugg estions contained in [32], where the authors
conclude that protein structure remains toler ant to r esidue substitu tions as long as th e
hydropathic profile of the sequence is preserved. Since water is an important factor in this

process, much effort has been directed towa rds analyzing the influence of the proteins’
aqueous environment.
They way in which residue sequences encode 3D structures remains a fundamental question
in biology. One approach to understanding the fold ing process is to desi gn a pair of proteins
with maximum sequence identity but with differing folds. Therefore, the nonidentities must be responsible for determining which fold topology prevails and constitute a fold-specific folding code. The intentionally designed proteins G
A88 and G B88, with 88% sequence
identity but different folds and f unctions [32] are described here in the context of the fuzzy oil
drop model. Despite a large number of mutations which together bring sequence identity from
16% to 88%, G A88 and G B88 maintain their distinct wild-type 3-alpha and alpha/beta folds,
respectively. As the authors [32] claim, the 3D-structure determination of two monomeric proteins with such high sequence identity but different fold topology is unprecedented. The geometries of seven nonidentical residues (of 56 to tal) provide insight into the structural basis
for switching between 3- α and α /β conformations. The fuzzy oil drop model applied to these
two de novo designed proteins, to two wild-type pr oteins with intentionally modified
sequences as well as to two homologous prot eins, reveals the importance of hydrophobic core
structure. Our analysis proves that the hypothesis expressing the dominant role of
hydrophobic interactions in tertiary structural stabilization can be confirmed quantitatively.
Additionally the role of hydrophobic core in stab ilization of structures of natural proteins
modified (mutated) to converge to a point of high-level sequence identity while retaining their
respective wild-type tertiary folds, of natural proteins with common ancestry but with
differing structures and biological profiles shaped by divergent e volution as well as of natural
proteins of high struct ural similarity with no sequence si milarity and different biological
function was recognized as main mechanism for structure stabilization as expressed by fuzzy
oil drop model.
The fuzzy oil drop model posits a structure which consists of a hydrophobic core (central part
of the protein body) together with a sheath acting as a buffer zone between the hydrophobic
center and the hydrophilic surface. The role of water in the pr otein folding process and its
influence on the final structure of the protein remains a persistent subject in molecular biology
[31,33]; however, the question of generalizing the presented observations remains an open issue. The application of fuzzy oil drop mode l for amyloidosis mechanism is presented in
[34].

Acknowledgements

Many thanks to Jacques Chomilier for fruitful discussions. The Authors are also grateful to
Piotr Nowakowski and Anna Śmietańska for technical aid. Th is work was funded by the
Collegium Medicum grant K/ZDS/006363.
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