Triana et al., IJOAR, 2018 1:13
Research Article
IJOAR (2018) 1:13
International Journal of Aging Research
(ISSN:2637-3742)
Deciphering the longevity of the mole-rats
L. Triana1, G. Cocho2, R. Mansilla3 and J.M. Nieto-Villar4*
1
Complete Pharmaceutics, Florida, United States of America
Instituto de Física de la UNAM, México
3
Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidades, UNAM, México.
4
Department of Chemical-Physics, A. Alzola Group of Thermodynamics of Complex Systems of M.V.
Lomonosov Chair, Faculty of Chemistry, University of Havana, Cuba.
2
ABSTRACT
A theoretical model of a nonlinear network that outlines the general aspects of mole-rat resistance to age-related diseases, such
as cancer and the action of ROS was elaborated. According to
our conjecture, it was shown that the protection is established
because hyaluronic acid of high molecular mass forms a non-linear network of interactions. That network leads to self-organization away from the thermodynamical equilibrium, which appears
through a “irst order” phase transition as a supercritical bifurcation of Andronov-Hopf type. Finally, it is shown how the rate of
entropy production is a Lyapunov function of the dynamics of the
process.
Keywords:
mole-rat
hyaluronic acid
ROS
Biological phase transition
Entropy production rate as a Lyapunov function
*Correspondence to Author:
J.M. Nieto-Villar
Department of Chemical-Physics,A. Alzola Group of Thermodynamics of Complex Systems of M.V. Lomonosov Chair, Faculty of Chemis
try, University of Havana, Cuba.
Email: nieto @ fq.uh.cu
How to cite this article:
L. Triana, G. Cocho, R. Mansilla
and J.M. Nieto-Villar. Decipheringthe longevity of the mole-rats. Inter
national Journal of Aging Research,
2018, 1:13
eSciPub LLC, Houston, TX USA.
Website: http://escipub.com/
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Triana et al., IJOAR, 2018 1:13
1. Introduction
equilibrium.
Longevity and aging remain one of the most
captivating and intriguing topics of human
knowledge. Despite all the achievements in the
biomedical sciences, the mechanism for aging
processes is still very unknown.
The paper is organized as follows: in Section 2
we propose a non-linear network model.
Section 3 focuses on the analysis of the
ordinary differential equations model derived
from the previously proposed mechanism,
including quantitative simulations and stability
analysis. The development of a thermodynamic
framework, based on the rate of entropy
production is presented in Section 4. Finally,
some comments and remarks are presented.
Mole-rats represent an ideal model for the
study of the aging process [1], as well as, to
understand
the
so-called
degenerative
diseases such as cancer [2, 3]. As a fact, the
journal Science named the naked mole-rat
"Vertebrate of the Year" for 2013 [2].
2. A nonlinear network model of mole-rat
The mole-rat is the longest known living rodent
and is a unique model of successful aging that
shows
attenuated
decreases
in
most
physiological functions [4]. In addition to their
longevity, mole rats show unusual resistance to
cancer [1]. More than this, the mole rat can
tolerate high levels of oxidative stress and have
mechanisms to prevent age-related diseases,
such as cancer, diabetes, and cardiovascular,
brain, and liver diseases, as well as many
infections [5, 6, 7].
Xiao Tian et al. [10] found that naked mole rat
fibroblasts secrete high molecular weight
hyaluronan ( HA ), which is five times larger
than the human or the mouse. High molecular
weight hyaluronan accumulates abundantly in
mole rat tissues due to the decreased activity of
degrading enzymes and a unique sequence of
hyaluronan synthase 2 (HAS2). In addition,
mole rat cells are more sensitive to signaling,
since naked mole rat cells have a higher affinity
than those of the mouse or the human cells.
The question that has puzzled the scientific
community for decades is: Why does the
human being, the mouse and the rat develop
cancer, but the mole rats do not or rarely do it?
It is well known that mole rats live in conditions
of hypoxia [11] and that they tolerate extreme
conditions such as anoxia [12]. During chronic
hypoxia, high levels of reactive oxygen species,
ROS, are induced, which may be associated
with a normal physiological response to the
imbalance in oxygen supply and demand or
environmental stress [13]. The hypoxia
inducible factor, HIF, is a transcription factor
that regulates the cellular response to hypoxia
and acts as a regulator of oxygen homeostasis
[14]. The system of HIF transcription [14] and
hypoxia are the major determinants in
angiogenesis and regulate, for instance the
processes of tumor invasion.
It is well known that there are multiple factors
that influence the biology of cancer [8] and
aging [9]. Therefore the mole rat is an
appropriate animal model, because of the
mechanisms they possess to reach a greater
longevity, resistance to hypoxia and to cancer.
These mechanisms could be taken as a
reference for studies of human cancer and
degenerative diseases [1, 2, 3].
The aim of this work is to show, through a
simple theoretical model, the mechanism of
resistance of the mole rat to age-related
diseases such as cancer and the action of
ROS. For this we establish as conjecture that:
Protection is established because hyaluronic
acid of high molecular mass ( HA ) conforms a
non-linear network of interactions that lead to
self-organization outside the thermodynamical
Chronic hypoxia inevitably leads to an increase
in glucose uptake and the accumulation of its
metabolites; consequently, hyaluronic acid will
be degraded by some hyaluronidases (HYAL16) or by ROS in fragments of different sizes
[15]. These low molecular weight hyaluronic
acid fragments serve as tissue repair signals,
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Triana et al., IJOAR, 2018 1:13
including signals of cell proliferation, cell
survival and angiogenesis, which lead to the
initial proliferation of the underlying cells [16].
It is well known that the mole rat can tolerate
high levels of oxidative stress [17] and exhibits
a high resistance to cancer [18, 5] due to its
capacity in the production of high molecular
weight hyaluronic acid [10]. In fact, it has been
found that ROS levels in moles are lower
compared to rats [19].
Based on what was discussed above, an
integrated framework according to the network
structure shown in Figure 1 is proposed.
Fig. 1. The nonlinear network model of mole-rat
In the model, A represent the oxygen
concentration, B , the high molecular weight
hyaluronan ( HA ) concentration, which is taking
as the control parameter, x are the
concentration of ROS spices, y are the
concentrations of the low molecular weight HA ,
z are the populations of the cancer cells and
ncp represent the concentration of the noncancer products.
Step 1 is related to the auto-catalytic formation
of reactive ROS oxygen species, ( x ) because
chronic hypoxia induces high level of ROS [13].
Step 2 shows the degradation of the hyaluronic
acid by ROS in fragments of different sizes ( y )
[15]. Step 3 shows the formation of tumor cells
( z ) from fragments of different sizes of
hyaluronic acid [16]. Step 4 shows the spread
of the tumor promoted by the action of ROS
[20]. Finally, step 5, outlines the protective
action of high molecular weight of hyaluronic
acid ( B ) [11]. Considering that the high
molecular weight accumulates abundantly in
mole-rat tissues [11] we take as the control
parameter.
The constants for the model proposed (see Fig.
1) were chosen empirically trying to have a
greater generality and simplicity as possible, so
we
have:
k1 = 4.7 ml/(mmol s) , k2 = 1 ml/(mmol s) , k3 = 1 s-1 ,
k4 = 1 ml/(mmol s) , k5 = 2 ml/(mmol s) .
3. Mathematical model, stability analysis
and numerical simulations
Mathematical models represent an adequate
way to formalize knowledge of living systems
obtained through a Systems Biology approach
[21, 22]. These types of models make possible
the description of important regularities and are
useful to provide effective guidelines for the
development of therapies, drugs and clinical
decision making.
The network model (Fig. 1) we propose is a
qualitative representation of the action of high
molecular
weight
hyaluronan
( HA )
concentration. We use the mathematical
methods of chemical kinetics to reduce the
network to a system of ordinary differential
equations such as
dx
= 4.7 xA − xz − xB
dt
dy
= xB − y
dt
dz
= y − 2 zB
dt
(3.1)
Quantitative value for each constant has been
empirically obtained. Fixed points, stability and
bifurcations analysis were calculated using the
standard
procedure
[23,24,25].
Control
parameters were represented by the high
molecular weight HA accumulates abundantly
in mole-rat tissues [11]. The corresponding
stationary state is:
xss =
47
5
A − 2B, yss =
47
5
47
AB − 2B2 , zss = 10
A− B
(3.2)
The characteristic equation as a function of the
eigenvalues is
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+ ( 2B + 1) + 2B − B ( 2B −
3
2
47
5
A)
Bc = 1.5667 A − 0.33333
Triana et al., IJOAR, 2018 1:13
(3.3)
(3.4)
and we find that the periodic oscillations occur
product of a supercritical Andronov-Hopf
bifurcation [23], where the critical value of the
control parameter is obtained from the following
equation:
COPASI v. 4.6.32 software was used. In Fig. 2
is shown the dynamic behavior for the system
(3.1).
For hypoxia condition, A = 1 , is obtained that:
Bc = 1.2334 . For simulating network model,
Fig. 2. Time series of the proposed model (see Fig.1) for different values of the control parameter
B : a. B Bc = 1.5 , b. B Bc = 1.23 , c. B Bc = 1.2 ; x (red), y (blue); z (green).
As observed, for the value of B Bc = 1.5 (see
Fig.2a) a stationary stable state appears, which
guarantees low levels of ROS ( x ) and the
tumor cells ( z ). For values of B Bc = 1.23 (see
also allow the system to perform various
functions, including control and regulation.
In Fig.2c, it is observed that a small decrease in
the concentration of B ( B Bc = 1.2 ), leads to
Fig.2b) due to the supercritical Andronov-Hopf
bifurcation appear periodic oscillations and the
same phenomenology observed in Fig.2a is
here maintained.
an increase in the concentration of ROS
species ( x ), which suggests that the
robustness of the action of HA not only comes
given that there is a critical concentration Bc of
This dynamic behavior leads to selforganization outside the thermodynamic
equilibrium. At macroscopic scales, the selforganization and the complexity exhibited by
dynamic systems are manifested through
oscillations in time and / or space. In biological
systems, these oscillations are usual [26], and
they do not only guarantee robustness [27], but
HA that guarantees self-organization, but also
that there must be a fine regulation of it.
4. Thermodynamics framework
As we know from thermodynamics irreversible
processes [28] for a chemical reaction the
entropy production can be evaluated as:
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(4.1)
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Triana et al., IJOAR, 2018 1:13
where A , according to De Donder and Van
Rysselberghe [29], represents the affinity and
the term
is the reaction rate. The formula
(4.1) could be rewritten [30] for the k-th
reaction as
(4.2)
Where
are the forward and
backward reaction rates respectively. The
whole entropy production rate
for the
network model (Fig.1) can be evaluated as
The network model proposed for the mole rat
generalizes, at least qualitatively, the main
characteristics of the regulatory action of high
molecular weight hyaluronic acid, as well as the
resistance of age-related diseases such as
cancer and the action of ROS.
In summary, in this paper we arrive at the
following theoretical conclusions:
•
(4.3)
In a previous work [31] we have shown that the
rate of entropy production is a Lyapunov
function, in fact we extended this formalism to
the development of cancer [32, 33, 34, 35, 36,
37]. Thus, we have the entropy production per
unit time meets the necessary and sufficient
conditions for Lyapunov function [30], such that
(4.4)
where is the vector of control parameters.
The Eulerian derivative (4.4) must hold:
where
(4.5)
;
( B ) is
related with concentration
of high molecular weight hyaluronan. Taking
into account (4.2) and (4.3), we can write the
whole entropy production rate
for the
network model (Fig.1) as a function of control
parameter B as
(4.6)
Then it fulfills that
(4.7)
As the control parameter B is a concentration
of high molecular weight hyaluronan a reactant,
dB
such as:
, that
0 , then it fulfills that:
dt
allows us to affirm that the rate of entropy
production is a Lyapunov function.
•
•
It was shown, according to our
conjecture, that the protection that the
moles rats have is established because
the high molecular weight hyaluronan
conforms to the nonlinear network of
interactions that lead to self-organization
far from thermodynamical equilibrium
and behaves according to the rules of a
"first order” phase transition through a
supercritical bifurcation of AndronovHopf type. In other words, oscillations
grant high robustness and complexity.
There must be a critical concentration of
the high molecular weight of hyaluronic
acid, such that it guarantees the selforganization and a fine regulation of the
process.
With the hyaluronic acid as the control
parameter of the system, it was shown
that the rate of entropy production is a
Lyapunov function. That is, it provides
the directionality of the process
We hope that the current theoretical framework
will provide a better understanding of aging
processes and cancer and will contribute to
improving the duration of human health,
longevity, as well as the search for optimal
pathways for future treatments.
Acknowledgements
Prof. Dr. A. Alzola in memoriam. We would like
to thank Prof. Dr. Jacques Rieumont for support
and encouragement for this research. One of
the authors (JMNV) thanks the CEIICH and the
Institute of Physics of the UNAM Mexico for the
warm hospitality and the financial support by
DGAPA/DF A/2210/2017. Also, we appreciate
5. Conclusions and remarks
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Triana et al., IJOAR, 2018 1:13
the financial support provided by Dr. Gregory
Gaiser, CEO of Complete Pharmaceutics.
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Ricardo Mansilla