Modeling of the Behavior of Ca Ions as Messengers

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Proceedings of The First World Congress on Biomimetics
December 9–11, 2002, Albuquerque, New Mexico
Copyright © 2002 by Biomimetics

Modeling of the Behavior of Ca Ions as Messengers





Professor Mihail D. Nicu, MD, Ph.D., Romanian Academy of Medical Sciences,
Bucharest, Romania
Sorin G. Popa, Ph.D., MAGNIM, Inc., Albuquerque, NM
Cristina Maria Dabu, Ph.D., Master Computers SRL





ABSTRACT

Cellular activity demonstrates the influx and mobilization of Ca ions from deposits either
through the action potential or through the coupling of a messenger I with specific
receptors. The behavior of messenger Ca ions has been modeling using MATLAB 4.2
and SIMULINK 1.3 software. The modeling was built taking into consideration the
description of the biologic process. Furthermore, the study of a number of laboratory
experiments regarding the behavior of intracellular Ca ions has been considered. The
models have been then tested for high fidelity compared with the real processes and their
performance has been validated.




In conditions of cellular rest the Ca
2+
concentration is maintained at values below 10
-7

mol/l, due to the existing equilibrium between the Ca
2+
flux and influx. Ca2+ influxes
could come from outside the cell, through I
L
, I
SA
channels, through messengers I, or
through G proteins from the receptor complex, or through other secondary messengers
(cAMP, cGMP, IP4). Another source for the Ca
2+
influx is the deposits of bond Ca
2+

within the cell, represented by mitochondria or by the endo(sarco)plasmatic reticulum.
The increase of the concentration of free cytoplasmatic Ca
2+
is compensated (during
cellular rest) by equivalent fluxes either towards outside (Ca
2+
ATPasic pump, operated
by other messengers II and the 1/3 Na
+
/Ca
2+
antiport system), either towards deposits
(recapture through Ca
2+
ATPases).

Cellular activation, either through the action potential (AP), or through the coupling
action of a messenger I with specific receptors, stimulates the flux and the mobilization
of Ca
2+
from deposits. When the concentration of free Ca
2+
from the cytoplasm goes
beyond the limit value of 10
-5
mol/l, the cellular response occurs, triggered by Ca
2+
as
messenger II.


Proceedings of The First World Congress on Biomimetics
December 9–11, 2002, Albuquerque, New Mexico
Copyright © 2002 by Biomimetics

As a function of the receptors involved in the process as well as the path followed, cell’s
responses could lead to effects such as: cAMP and cGMP degradation, cAMP and cGMP
formation, glycogenolysis, synaptic release of neuromediators, protein synthesis, etc.

Through the effects of activating other messengers II, the Ca2+ - CaM complex creates
the possibility of a modulating interaction between two or more intracellular signaling
lines, that are activated by receptors and have significant effects on the final cumulative
response of the cell.

When a cell is at rest, the concentration of free cytoplasmatic Ca2+ is maintained at
values below 10-7 mol/l and the system is described by the following equations:


FFATPCaFATPCa
Q
++

22
ERCaMitCaGCaMsgCaICaICa
L
QQQQQQQ
dt
Cad
ISAL
++++++
−+++++=
+
222222
][
2


0
][
2
=
+
dt
Cad
L




Where:

[Ca
2+
L
] = concentration of free Ca
2+
within the cytoplasm of a nerve cell, at rest;
Q
Ca2+IL
= influx of extracellular Ca
2+
through ionic channels of type I
L
;
Q
Ca2+ISA
= influx of free Ca
2+
, extracellular through ionic channels of type I
SA
;
Q
Ca2+MsgI
= influx of free Ca
2+
, extracellular, through messengers I;
Q
Ca2+G
= influx of free, extracellular Ca
2+
through G proteins;
Q
Ca2+Mit
= flux of free Ca
2+
from mitochondrial deposits;
Q
Ca2+ER
= flux of free Ca
2+
from the endoplasmatic reticulum;
Q
Ca2+FATP
= flux of free, intracellular Ca
2+
through the ATPasic pump;
Q
Ca2+FFATP
= flux of free, intracellular Ca
2+
, recaptured by Ca
2+
ATPases and deposited in
mitochondria.



Figure 1 below shows the state chart for modeling Ca
2+
in a neuronal cell at rest.


Proceedings of The First World Congress on Biomimetics
December 9–11, 2002, Albuquerque, New Mexico
Copyright © 2002 by Biomimetics



Figure 1. State chart for Ca
2+
during cellular rest

For developing the model in SIMULINK, to describe the behavior of intracellular Ca
2+
as
messenger II, the following things were considered:
-description of the biological process
-analysis of great number of lab tests regarding the behavior of Ca
2+
, including:
1. substances and equipment used
2. experimental methods
3. data acquisition protocols
4. tables and charts containing results of the analyzed tests

The models that were built are characterized by the fact that, for input data that is similar
(from the point of view of equivalence with the real world) to measurable input data for
the real system in laboratory conditions, the output data, from point of view of values and
evolution in time, was very close to the experimental data obtained from the lab tests.
Also, the obtained models have been verified, to establish their validity and adjustments
were made where it was required, for a higher fidelity of the models.

The models were developed with MATLAB 4.2 for Windows and SIMULINK 1.3. In
their development, the following were considered:

1. Intracellular Ca
2+
is one of the most important messengers II, having a decisive role
in secretion, motility, intermediary metabolism, cellular division, and cell death;

Proceedings of The First World Congress on Biomimetics
December 9–11, 2002, Albuquerque, New Mexico
Copyright © 2002 by Biomimetics

2. Intracellular Ca
2+
concentration is very important in information processing at
neuronal level;
3. The mechanisms for regulation of Ca
2+
distribution within a nerve cell include mainly
non-linear processes, whose kinetics depends both on time and space;
4. Not all the sub-systems that contribute to the regulation of intracellular Ca
2+

concentration operate at the same rate. Some are rapid systems, while others are slow
systems, with delays and idle periods;
5. Research demonstrated the existence of more Ca
2+
transport sub-systems at neuronal
level: mitochondrial sub-system, endo(sarco)plasmatic reticulum sub-system, ionic
channels transportation, Ca
2+
ATPases transportation and transport through Na
+
/Ca
2+

ion exchangers;
6. Lab tests carried out on mouse hippocampus cells demonstrated that, following and
action potential, intracellular Ca
2+
concentration could reach the value of 1mM,
while, at rest, intracellular Ca
2+
concentration is about 0.1 mM. Lab tests analysis,
performed with the FURA-2 system have shown that the induction of an intracellular
depolarization, following 10-20 action potentials, increases the level of intracellular
Ca
2+
concentration within soma and proximal apical dendrites from 0.02-0.05 mM to
0.1-0.2 mM. The time required for the concentration level to come back to the initial
value was about 100 ns. Other similar lab tests analyses have shown that the level of
intracellular Ca
2+
concentration could increase by 400-500% as a response to an
electric pulse applied for 500 ms, with a comeback to the initial value period of 5 s.
7. Fluctuation of the Ca
2+
concentration at cell level depends on:
-the volume of the substance where the process takes place;
-local diffusion coefficient
-geometry of the elements and structures analyzed.

The results of the simulation are shown Figures 2 and 3.



Proceedings of The First World Congress on Biomimetics
December 9–11, 2002, Albuquerque, New Mexico
Copyright © 2002 by Biomimetics

Figure 2. Simulation results with low variation of Ca
2+
concentration

Figure 3. Simulation results with higher variation of Ca
2+
concentration



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