Research Article
Comparative Study of Metaheuristics for the Curve-Fitting
Problem: Modeling Neurotransmitter Diffusion and Synaptic
Receptor Activation
Jesús Montes, Antonio LaTorre, Santiago Muelas, Ángel Merchán-Pérez, and José M. Peña
DATSI, ETS de Ingenieros Inform´ aticos, Universidad Polit´ ecnica de Madrid, Campus de Montegancedo,
28660 Boadilla del Monte, Madrid, Spain
Correspondence should be addressed to Jes´ us Montes; jmontes@f.upm.es
Received 22 October 2014; Revised 10 April 2015; Accepted 15 April 2015
Academic Editor: Jinde Cao
Copyright © 2015 Jes´ us Montes et al. Tis is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Synapses are key elements in the information transmission in the nervous system. Among the diferent approaches to study
them, the use of computational simulations is identifed as the most promising technique. Simulations, however, do not provide
generalized models of the underlying biochemical phenomena, but a set of observations, or time-series curves, displaying the
behavior of the synapse in the scenario represented. Finding a general model of these curves, like a set of mathematical equations,
could be an achievement in the study of synaptic behavior. In this paper, we propose an exploratory analysis in which selected curve
models are proposed, and state-of-the-art metaheuristics are used and compared to ft the free coefcients of these curves to the
data obtained from simulations. Experimental results demonstrate that several models can ft these data, though a deeper analysis
from a biological perspective reveals that some are better suited for this purpose, as they represent more accurately the biological
process. Based on the results of this analysis, we propose a set of mathematical equations and a methodology, adequate for modeling
several aspects of biochemical synaptic behavior.
1. Introduction
Most information in the mammalian nervous system fows
through chemical synapses. Tese are complex structures
comprising a presynaptic element (an axon terminal) and a
postsynaptic element (a dendritic spine, a dendritic shaf, an
axon, or a soma) separated by a narrow gap known as the
synaptic clef (see Figure 1). Te neurotransmitter is stored
in synaptic vesicles located in the presynaptic terminal. For
release to take place, the membrane of one or more vesicles
must fuse with a region of the presynaptic membrane, the
active zone, and lining the synaptic clef. On the opposite
side, the postsynaptic membrane is populated by specifc
receptors.
Multiple factors infuence the difusion of neurotransmit-
ter molecules and their interaction with specifc receptors
[1–3]. Te initial concentration of the released neurotrans-
mitter in the extracellular space depends on the volume of
the synaptic clef. Te subsequent difusion of neurotrans-
mitter molecules outside the clef may be infuenced by the
geometrical characteristics of the membranes that surround
the synaptic junction, and by the presence and concentration
of transporter molecules. However, direct observation of the
various synaptic events at the molecular and ultrastructural
levels in vivo or in vitro is rather difcult, if not impossible.
Simulation approaches are thus useful to assess the infuence
of diferent parameters on the behavior of the synapse (e.g.,
[4, 5]).
Simulation approaches in neuroscience have considered
diferent models, scales, and techniques, according to the
phenomenon being studied. Biochemical processes, such as
neurotransmitter difusion, require Monte Carlo particle-
based simulators like MCell [6, 7], ChemCell [8], or Smoldyn
[9, 10]. Tese simulation techniques allow computational
neuroscientist to reproduce these biological processes in a
manner that they can be thoroughly observed, systematically
Hindawi Publishing Corporation
Abstract and Applied Analysis
Volume 2015, Article ID 708131, 16 pages
http://dx.doi.org/10.1155/2015/708131