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Molecular model for hydrated biological tissues

Article  in  Physical Review E · June 2015

DOI: 10.1103/PhysRevE.91.063310

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PHYSICAL REVIEW E 91, 063310 (2015)

Molecular model for hydrated biological tissues

Erika Tiemi Sato,1 Alexandre Reily Rocha,2 Luis Felipe das Chagas e Silva de Carvalho,3

Janete Dias Almeida,4 and Herculano Martinho1,*

1Universidade Federal do ABC, Av. dos Estados, 5001, Bangu, 09210-580, Santo André-SP, Brazil
2Instituto de Fı́sica Teórica, Universidade Estadual Paulista (UNESP), R. Dr. Bento Teobaldo Ferraz, 271 - Bloco II, Barra-Funda,

01140-070, São Paulo-SP, Brazil
3FOCAS Institute, Dublin Institute of Technology, Camben Row, Dublin 8, Ireland

4Depto. de Biociências e Diagnóstico Bucal, Instituto de Ciência e Tecnologia, Campus São José dos Campos,
Universidade Estadual Paulista (UNESP), Av. Eng. Francisco José Longo, 777, Jardim São Dimas, 12245-000,

São José dos Campos-SP, Brazil
(Received 28 October 2014; published 25 June 2015)

A density-functional microscopic model for soft tissues (STmod) is presented. The model was based on a
prototype molecular structure from experimentally resolved type I collagen peptide residues and water clusters
treated in periodic boundary conditions. We obtained the optimized geometry, binding and coupling energies,
dipole moments, and vibrational frequencies. The results concerning the stability of the confined water clusters,
the water-water, and water-collagen interactions were successfully correlated to some important experimental
trends of normal and inflammatory tissues.

DOI: 10.1103/PhysRevE.91.063310 PACS number(s): 31.15.A−, 87.14.em, 87.17.Aa, 87.64.kp

I. INTRODUCTION

The role of water in biological systems is still, in many
cases, an enigma even though this molecule is an integral part
of many biomolecular complexes. In particular, proteins have
much of their properties governed by interactions with water
[1]. Leikin et al. [2] have shown that hydration force effects
resulting from the energetic cost of water rearrangements
near a collagen surface display distinguished features in its
Raman spectra. We have shown, in a previous study [3], that
water behaves differently in healthy and pathological tissues.
Vibrational modes analysis compared to literature results
[4,5] showed that the inflammatory process led to changes
in the high-wave number spectral region related to collagen
and confined water. Furthermore, intracellular hydration can
be of great relevance in cancerous processes, since cancer
cells contain more free water than normal cells. The cellular
hydration increases with increasing degree of malignancy
[6,7]. Hydropic degeneration (excess of water absorption by
the epithelial tissue) and biochemical redox reactions are two
important characteristics of the inflammatory process.

The prevalence of typical water clusters in inflammatory
tissues is a known event reported in the literature [8]. Cibulsky
and Sadlej [5] observed that the OH-stretching vibrations
region of Raman spectra are related to local structures and
interactions of the hydrogen-bond networks, so each water
cluster has a characteristic Raman spectrum. de Carvalho
et al. [3] pointed out that this could be the origin of the
discriminating power of the high-wave number region closely
related to the hydropic degeneration process in inflammatory
fibrous hyperplasia. Raman spectroscopy studies performed
by Gniadecka et al. [9] found an increased amount of the non-
macromolecule bound, tetrahedral water in photo-aged and
malignant tumors of the skin compare to normal tissues. These
experimental results indicated the relevance of understanding
the role of electrons, protons, and hydration water in tissues.

*herculano.martinho@ufabc.edu.br

Computational simulations are widely used to study and
make predictions concerning a broad variety of systems
ranging from pharmacology to engineering fields [10–12].
Atomistic models based on quantum mechanics calculations
have the greatest predictive capability for materials properties.
However, due to their inherent complexity (aperiodicity
and large number of atoms), detailed atomistic models for
biological tissues are absent in the literature. Such models
would be useful to understand physical and biochemical
properties of tissues. For example, little is known about
the underlying mechanisms of cell migration in wound
healing, specially the modulating role of mechanical tension
at the micro-environmental scale [13]. Usually finite-element
classical approaches have been applied to simulate mechanical
characteristics of soft tissues such as skin [14]. However, many
physical properties have not been satisfactorily simulated by
these conventional models [15,16]. Monte Carlo methods
have been generally considered as the standard to simulate
light propagation in heterogeneous tissues and to validate
the results obtained by other models. The main drawbacks
of this method are the extensive computational burden
[15], absence of realistic phase function, and elastic light
scattering models [16]. Moreover, the explicit structure of
water and its interactions with the neighbors are not accounted
for.

The dynamics of atoms, molecules, electrons, protons,
and hydration water using quantum mechanical approaches,
to the best of our knowledge, have only been studied for
isolated or solvated biomolecules. Simulation models reported
are mostly classical [17–20] or hybrid models [21]. Of all
proteins present in our body, collagen is the most abundant
and for this reason has been exhaustively studied. An atomistic
model based on this important biomolecular complex would
enable the study of the molecular interactions which would be
present; to quantify the relative strength of each interaction; to
perform dynamical simulations; and to predict properties as,
e.g., electronic structure, transport, and absorption, emission,
and vibrational spectra with high degree of accuracy. To
correctly describe soft tissues and be computationally viable

1539-3755/2015/91(6)/063310(6) 063310-1 ©2015 American Physical Society

http://dx.doi.org/10.1103/PhysRevE.91.063310


SATO, ROCHA, DE CARVALHO, ALMEIDA, AND MARTINHO PHYSICAL REVIEW E 91, 063310 (2015)

the atomistic model should be small enough and include
water-water and water-molecule effects.

In the present work a microscopic model for soft biological
tissue based on Density Functional Theory (DFT) is presented.
This model, named Soft Tissue model (STmod) retains some
fundamental atomic connectivity based on the collagen fibrils
constitution. However, it is important to stress that STmod is
not a simple solvating collagen model. The stability of some
proposed variations of the model was studied, and compared
to relevant experimental results.

II. METHODOLOGY

Figure 1(a) shows a general scheme of a real connective soft
tissue. The different collagen types form large fibrillar bundles.
These collagen fibrils are semi-crystalline aggregates of colla-
gen molecules and water (>1000 amino acids). Approximately
60% of the dry tissue has proteic constitution (collagen fibrils)
[22]. Figure 1(b) shows the dimension scale of STmod. In order
to built the STmod we associated the set of collagen fibers
to a reticulated set of unit cells whose internal constitution
should be appropriately chosen. In our approximation the
complexity of the real tissue was replaced by this periodic set
using periodic boundary conditions (PBC). PBC are usually
chosen for approximating a very large (or infinite) system by
using a small part of it (unit cell) for theoretical modeling
of both periodic or aperiodic systems. Considering typical
collagen fibers dimensions and the relative composition of
∼60% of fibers in the tissue, one could estimate typical tissue
is composed by ∼1012 STmod unit cells/mm2. The PBC
approximation could be justified by this estimate. The STmod
unit cell was built starting with an experimentally resolved
hydrated collagen type I structure obtained from the Protein
Data Bank [23]. A specific peptide sequence of this structure
was cut retaining proline, glycine, and hydroxyproline amino
acids which enclosed some water molecules. An example of
structure enclosing four water molecules is shown in Fig. 1(c).
The criteria used to choose this specific peptide sequence were
based on (i) the presence of water molecules confined in the
original structure; (ii) the presence of residues of amino acids;
(iii) the viable number of amino acids with respect to time
of calculation (typically ∼100 atoms). Two variants of this
small unit were chosen (labeled C and D structures). The C

structure has orthorhombic symmetry (P 212121 space group);
unit cell parameters a = 13.5 Å, b = 11.5 Å, and c = 10.5 Å,
and internal cage volume (oblate spheroid) Vc = 1,857.3 Å3

(see Table I). The corresponding dry structure C0 is show
on the left-hand side of Fig. 2. To build several hydrated
models, an specific water clusters were inserted in the center
of the structure. Water cluster structures (H2O)n (1 � n �
8)1 were chosen based on the TIP4P model [24] from the
Cambridge Cluster Database [25]. Therefore, we label the
STmod structures Cn (0 � n � 8). The effect of the presence
of an external hydration shell was checked on the C1 structure.

1It is possible the existence of more than a single symmetry for the
same atomic set for n � 5. Thus, we followed the choice of [5] and
considered only the structures (H2O)5-cyclic,(H2O)6-cage, (H2O)7-low,
and (H2O)8-S4.

FIG. 1. (Color online) (a) Structural scheme of a connective
tissue showing the collagen fibers and the fibrils. These are constituted
by water and collagen molecules. (b) The construction of the STmod
unit cell compared the original collagen fibers structure. (c) STmod
unit cell example (C4 structure) chosen from a experimentally
resolved hydrated peptide structure. (d) C4 structure enclosing four
water molecules clusters. In (c) and (d) hydrogen bond inside water
clusters were indicated by yellow. Hydrogen, carbon, nitrogen, and
oxygen atoms were in white, green, blue, and red, respectively.

063310-2



MOLECULAR MODEL FOR HYDRATED BIOLOGICAL TISSUES PHYSICAL REVIEW E 91, 063310 (2015)

TABLE I. Parameters for simulated structures. The space group
was P 212121 (orthorhombic) in all cases. The unit cell lattice
parameters (a,b,c), the cage volume (Vc), the number of internal
(cage), and external water molecules are also shown.

parameter Cn C1s D0,D1

a (Å) 13.5 15.0 17.4
b (Å) 11.5 12.5 13.3
c (Å) 10.5 20.0 9.8
Vc = (Å3) 1,857.3 1,857.3 182.8
cage waters 0 < n < 8 1 1
external waters 0 10 0

Ten external water molecules were added to the C1 structure
(C1s structure) shown in the center of Fig. 2. Another structural
variant is the compact version of C structure, with unit cell
parameters a = 17.4 Å, b = 13.3 Å, c = 9.8 Å, and Vc =
182.8 Å3. Only dry (D0, right of Fig. 2) and monohydrated
(D1) structures were considered in the present study. Each
cell was replicated [see Fig. 1(d), for example] in order to
describe the soft tissue. It is important to stress that Cn, C1s , and
D1 structures represent the most common sites where water
clusters could be present in fibrils and collagen [23,26,27].

Molecular mechanics models are useful for simulations of
conformal energies and non-covalent interactions of complex
molecular systems [28]. The MMFF94s force field [29] uses
the van der Waals term and includes cubic and quartic terms
in the bond stretch, and cubic terms in angle bending potential
energy. MMFF94s produces relatively flat dynamically aver-
aged structures [29]. The Cn models were pre-optimized in a
first step using molecular mechanics with the MMFF94s force
field [29] implemented in the Avogadro software [30]. The
D models were optimized in a first step using Hartree Fock
(HF) with the 6-31 + g(2d) basis implemented in the Gaussian
package [31]. HF methods are one of the least computationally
demanding quantum methods.

Finally, Density Functional Theory (DFT) [32,33] was used
in order to obtain the equilibrium geometries and harmonic
frequencies. The convergence of the calculation was also
checked by computing the total energy as a function of unit
cell volume variation. We notice that a converged energy value
(99.2% of the initial value) was found for 5% unit cell volume
variation. The confinements were implemented in the CPMD
program [34] using the BLYP functional [35] augmented with
dispersion corrections for the proper description of van der
Waals interactions [36,37]. For all simulations, the cutoff

FIG. 2. (Color online) C0, C1s , and D0 structures.

energy was considered up to 100 Ry. The wave functions
were optimized and then the vibrational modes were obtained
with Raman responses using the Hessian matrix. Finally, the
linear response for the values of polarization and polar tensors
of each atom in the system was calculated to evaluate the
eigenvectors of each vibrational mode. Harmonic frequencies
were compared to experimental Raman data for normal (NM)
and inflammatory (IFH) oral mucosa tissue (see Ref. [3] for
experimental details). The spectra were simulated as a convo-
lution of Gaussian lineshape peaks centered on the calculated
frequencies. The linewidth was chosen to be 20 cm−1.

III. RESULTS AND DISCUSSION

C0-normalized total energies for each structure are shown
in Fig. 3(a). We compared the energies of non-optimized
and geometry optimized structures. Since the non-optimized
structures retained the original experimental structural param-
eters, this comparison is of interest. In all structures the total
energy decreased by less than 20% with an increase in the
difference, the greater the water cluster size was. The results
show that a larger number of molecules per cluster lowers the
cluster energy. An exponential dependence on water content,

C1 C2 C3 C4 C5 C6 C7 C8 C1s D1

-8
-6
-4
-2
0
2
4

C1 C2 C3 C4 C5 C6 C7 C8

-0.8

-0.4

0.0

E 
(e

V
/a

to
m

)
[E

n-E
0]/E

0

0 2 4 6 8 10 12 14
0

10
20
30
40
50
60
70

(a)

(b)

(c)

C
ou

nt

FIG. 3. (a) Normalized total energy per atom for optimized and
non-optimized C structures. (b) Histogram for atomic coordinates
of C0 showing the effect of geometry optimization. (c) Binding EB

(open circle) and coupling EC (closed square) energies as defined in
Eqs. (2) and (3), respectively, for the various structures.

063310-3



SATO, ROCHA, DE CARVALHO, ALMEIDA, AND MARTINHO PHYSICAL REVIEW E 91, 063310 (2015)

n, according to

En − E0

E0
= −0.964 + 1.86e(− n

1.388 ) (1)

was observed [solid line in Fig. 3(a)]. It is important to
notice that all cluster structures were stable (En < E0). Park
et al. [38] analyzed structures and energies of the dimer to
heptamer water clusters using the revised empirical potential
function for conformational analysis. They realized that the
cyclic structures for water clusters are more favorable than
open structures in general, except for the heptamer case.
They also noted the more hydrogen bonds a cluster has, the
greater its stability. Thus, the stability of the chain of clusters
increases by adding a water molecule to the cluster. However
the energetic gain for C4 < C < C8 was �8%. It could be
stated the energetic gain was minimum for C > C4.

Figure 3(b) shows a histogram of atomic distances for
non-optimized and optimized C0 structures in order to compare
the effect of optimization in the experimentally determined
original atomic positions. The observed tendency was a
small displacement at �5% from their original arrangements.
However, it is important to stress that the original atomic
connectivity and symmetry remain unchanged.

Characterization of the inter-water molecule interactions,
and the interactions between confined water molecules and col-
lagen clusters was done by calculating the binding energy (EB)
and the coupling energy (EC), respectively. EB is defined by

EB = ESTmod − (
E0 + nEH2O

)
, (2)

and measures the average interaction between the free water
molecules and their environment. ESTmod, E0, and EH2O are
STmod unit cell, C0 or D0, and water molecule energies of
formation.

The interaction energy between the amino acid cage and
water cluster within the STmod unit cell can be estimated as

EC = ESTmod − (
E0 + EnH2O

)
, (3)

where EnH2O is the energy of the cluster composed by n water
molecules. Our definition differs from that of Ref. [39] by the
minus sign and normalization to n.

Figure 3(c) presents EB and EC for each structure. EB

increased monotonically with n. Similar behavior was ob-
served in the literature. Monotonically increasing energies as a
number of water molecules for confined water in single-walled
nanotubes was observed, e.g., by Wang et al. [39]. External
work needs be done to introduce the water clusters inside
the amino acid cage since EB > 0. Thus, proteins loci with
symmetry similar to Cn structure are not viable places to
catalyze the creation of water clusters. Even so, these cages are
feasible places for the insertion of water clusters. The solvation
of the C1 structure (C1s) does not contribute to decreasing EB .
The D structure containing one water molecule (D1) presented
the lowest EB . One concludes this compact structure is the
viable one to trap H2O molecules.

The coupling energy EC for Cn structures [Fig. 3(c)] was
found to be close to zero independent of the water content,
except for n = 4 and 8. We found the preferred cluster
structure to pack water molecules was the D1 one. Tetrahedral
C4 and icosahedral C8 water clusters appeared to have the
greatest positive EC . Thus, under basal conditions these

clusters will be weakly interacting with the C0 cage, which
implies in greater mobility. The coupling energy for the other
Cn structures were ∼1 meV, falling into the energy scale of
molecular vibrations. The D1 structure was the one more
strongly coupled to the D0 structure.

Properties of water clusters are fundamental for under-
standing water in biological systems [40]. Electrons between
biomolecular redox sites involve electron tunneling through
the intervening space, which can be facilitated, in part, by
aqueous proton movement in the reverse direction. The rate
of transfer depends on both the extent and the structure of the
intervening space. In particular, proteins have much of their
properties governed by interactions with water [1]. These,
for example, establish the free-energy landscape that deter-
mines their folding, structure, stability, and activity [41].
Structured water clusters near redox cofactors accelerate
electron transfer by producing strongly coupled tunneling
pathways between the electron donor and acceptor. More
generally, water molecules can facilitate or disrupt this process
through the degree of alignment of their dipoles and their
capability to form water wires [1,7].

The calculated dipole moments (μ) are shown in Fig. 4.
C1s and D1 displayed the greatest and lowest dipole moment,
respectively. The point charge q and μ, average interaction
potential is given by

U = −k2 q2μ2

3kBT r4
, (4)

where k is the Coulomb constant, T is the temperature, and r

the distance between the point charge and μ. From Fig. 4 and
Eq. (4) one concludes a moving electron will be more strongly
bound to the C1s structure. The D1 structure will trap traveling
electrons more weakly, favoring electron and small ion trans-
port. From these qualitative clues one expects sites with C sym-
metry to be the preferred ones to host physiological processes,
where large water clusters and strongly bonded electrons are
needed. The abundance of free tetrahedral water in tumor tissue
may be interpreted with our model framework considering that
solid tumors have a tendency to enhance the permeability and
retain large macromolecules (>40 kDa) [42]. On the other
hand, events where electron transport associated with lower hy-
dration levels are the rule, will take place on loci with D struc-
ture. These results confirmed the hypothesis that the structure

C0 C1 C2 C3 C4 C5 C6 C7 C8 C1s D0 D1
0

10

20

30

40

µ 
(D

)

Structures

FIG. 4. Total dipole moment (μ) for each structure.

063310-4



MOLECULAR MODEL FOR HYDRATED BIOLOGICAL TISSUES PHYSICAL REVIEW E 91, 063310 (2015)

2800 3000 3200 3400 3600

C8
C6
C5
C3
C2
C1
C1s

(10)

(9)

(8)

(7)

(6)

(5)(4)
(3)

(2)

D1

NM (a)(1)

C2
C0

C4
C7

 

In
te

ns
ity

 (a
rb

. u
ni

ts
)

Raman Shift (cm-1)

IFH (b)

FIG. 5. Raman spectra obtained for each confinement and the
experimental curves of normal (NM) (a) and inflammatory fibrous
hyperplasia (IFH) (b) tissues. Numbers (1) to (10) indicate the
vibrational bands discussed in the text.

of confined water alters in pathological tissues. The inflamma-
tory response would be specially influenced by this fact.

Figure 5 presents the experimental Raman spectra of normal
[NM, Fig. 5(a)] and inflammatory [IFH, Fig. 5(b)] oral mucosa
tissues, compared to simulated spectra from STmod models.
More experimental details concerning these data can be found
in Ref. [3] It is important to notice all experimental bands or
sub-bands where reproduced, except the one at 2840 cm−1.
This band is usually attributed to symmetric methyl group
stretching of lipids, and STmod did not take into account
the presence of lipids. The NM spectrum presented strongest
bands at 2933 cm−1 (band 2) that superposes two asymmetric
shoulders at 2880 (band 1) and 2965 cm−1 (band 3). The left
shoulder and the strongest peak were well reproduced by the
D1 vibrational modes. C5 and C6 contributed to the maximum
at 2933 cm−1. All clusters contributed to the right shoulder,
except C8 one. The band at 3010 cm−1 (band 4) was found to
be a signature of NM tissue since it was absent on IFH. This
band is a convolution of contributions from C1s , C2, C3, and
C6 clusters. IFH tissue [Fig. 5(b)] was characterized by the
presence of the strongest band at 2938 cm−1 (band 7) and two
symmetric shoulders at 2884 (band 6) and 2992 cm−1 (band
8). These bands were narrowed compared to NM ones. The
vibrational contributions from C0, C4, and C7 were enough
to explain this region since their Raman spectra did not
present the NM signature band at 3010 cm−1. The 3070 cm−1

(band 9) band was found to be a signature of IFH tissue
and only the C4 and C2 clusters presented this vibrational
mode. Finally, the broad OH vibrational spectral window
between 3070 and 3600 cm−1 (bands 5 and 10) appeared to
be a complex superposition of contributions from D1, C1s ,
C1 − C3, C5, C6,C8, and C0,C4,C7 clusters for NM and IFH
tissues, respectively.

IV. CONCLUSION

Protein-water interactions are known to play a critical
role in the function of several biomacromolecular systems
including collagen tissues [43]. Small changes in structure
and dynamical behavior of water molecules at the peptide-
water interface can effectively change both the structure and
dynamics of the protein function [44]. Thus, it was realized
that the presence of different water clusters plays an important
role in collagen properties.

The properties of the structures proposed within the STmod
framework enabled us to qualitatively correlate it to some
important trends observed experimentally in inflammatory tis-
sues while keeping the structure to a minimum. We found that
a tetrahedral C4 structure is weakly bound to the amino acid
cage, being it the smallest stable structure containing water
clusters. The EC discussion lead us to conclude that tetrahedral
water inside this structure has high mobility. This correlates
with literature findings reporting occurrence of tetrahedral
water in pathological tissues. The Raman data analysis also
corroborated these findings. These clusters are the loci of pos-
sible biochemical reactions in the inflammatory cascade where
strongly bound electrons play a role. We also found that D-like
cages with one water molecule trap electrons more strongly
and are thus suitable sites for water and small ion transport.

Moreover, improvements need to be implemented into the
STmod to describe others tissues. For example, small glycerol
or phospholipid molecules can be inserted surrounding the
unit cell to mimic the brick-and-mortar-type structure of
stratum corneum layer [45,46] of skin. A bidimensional
STmod with lipids in one side would also be realized to
simulate the dermis-hypodermis interface properties. Agents
as inflammatory mediators or specific phospholipids can also
be inserted in the structure and events as, e.g., inflammatory
conditions, emulsifier or moisturizing effects, could be studied
by molecular dynamics.

In summary, the STmod is a very promising model for more
complex physical and biochemical properties calculations
of tissues. Water or other biofluids microperfusion, Young’s
modulus at microscale, electron and proton transport, optical
and electronic spectra, vibrational (Raman and IR) spectra are
some examples of properties which could be calculated using
this model.

ACKNOWLEDGMENTS

The authors are grateful to the Brazilian agencies Fundação
de Amparo à Pesquisa do Estado de São Paulo (FAPESP),
Coordenação de Aperfeiçoamento de Pessoal de Nı́vel Supe-
rior (CAPES), and Conselho Nacional de Desenvolvimento
Cientı́fico e Tecnológico (CNPq) for financial support and
Multiuser Central Facilities of UFABC and CENAPAD-SP
for experimental and computational support, respectively.

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