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Evolutionary Intelligence to Stimulate Immune System

VIEWS: 9 PAGES: 12

									Evol. Intel. (2008) 1:133–144
DOI 10.1007/s12065-008-0010-z

 RESEARCH PAPER



Evolutionary algorithms to simulate the phylogenesis
of a binary artificial immune system
Grazziela P. Figueredo Æ Luis A. V. de Carvalho Æ
Helio J. C. Barbosa Æ Nelson F. F. Ebecken




Received: 12 November 2007 / Revised: 12 March 2008 / Accepted: 13 March 2008 / Published online: 29 April 2008
Ó Springer-Verlag 2008


Abstract Four binary-encoded models describing some                  as to maximize their profit. Numerical experiments and
aspects of the phylogenetics evolution in an artificial               conclusions are shown. These considerations present many
immune system have been proposed and analyzed. The first              similarities to biological immune systems and also some
model has focused on the evolution of a paratope’s popu-             inspirations to solve real-world problems, such as pattern
lation, considering a fixed group of epitopes, to simulate a          recognition and knowledge discovery in databases.
hypermutation mechanism and observe how the system
would self-adjust to cover the epitopes. In the second               Keywords Artificial immune systems Á
model, the evolution involves a group of antibodies adapt-           Evolutionary computation Á
ing to a given antigenic molecules’ population. The third            Artificial immune systems models
model simulated the coevolution between antibodies’ gen-
erating gene libraries and antigens. The objective was to
simulate somatic recombination mechanisms to obtain final             1 Introduction
libraries apt to produce antibodies to cover any possible
antigen that would appear in the pathogens’ population. In           The immune system (IS) is able to protect us from a number
the fourth model, the coevolution involves a new population          of pathogens. It also monitors the organism, searching and
of self-molecules whose function was to establish restric-           destroying anomalous cells. To perform such tasks, the IS
tions in the evolution of libraries’ population. For all the         must recognize a great variety of different compounds and
models implemented, evolutionary algorithms (EA) were                distinguish, among them, those which can remain in the
used to form adaptive niching inspired in the coevolutionary         organism and those that are to be eliminated. It is believed
shared niching strategy ideas taken from a monopolistic              that the IS identifies about 1016 foreign molecules [18],
competition economic model where ‘‘businessmen’’ locate              which means that it can identify any molecule [10].
themselves among geographically distributed ‘‘clients’’ so              The IS pattern recognition task is performed through
                                                                     surface receptor molecules of T and B cells. The identifi-
                                                                     cation of antigens in both these types of lymphocytes
G. P. Figueredo (&) Á L. A. V. de Carvalho Á N. F. F. Ebecken
                                                                     occurs differently. B cells recognize antigens through
Federal University of Rio de Janeiro - COPPE,
Rio de Janeiro, Brazil                                               immune globulins from its cell surface. T cells recognize
e-mail: gpfigueredo@gmail.com                                         only antigens presented by an antigen presenting cell
                                                                     (APC). The creation of these receptors and their capability
L. A. V. de Carvalho
                                                                     to cover all antigens have their origin in a very sophisti-
e-mail: meucorreioeletronico@gmail.com
                                                                     cated genetic mechanism. During the receptor’s formation
N. F. F. Ebecken                                                     process, the variation is caused by the combinatorial
e-mail: nelson@ntt.ufrj.br                                           associations among the receptors codifying genes and the
                                                                     hypermutation mechanism.
H. J. C. Barbosa
                 ´
LNCC, MCT, Petropolis, Brazil                                           The hypermutations occur in the lymph nodes’ germi-
e-mail: hcbm@lncc.br                                                 native centers. Thus, when an APC penetrates the lymph


                                                                                                                       123
134                                                                                               Evol. Intel. (2008) 1:133–144


node and shows an antigen to a T cell, or when a B cell             There are many possible combinations of the available
finds a pathogen and identifies it, that means the combi-          gene segments, which gives the IS the capability of pro-
nation was well succeeded. After the recognizing pattern is      ducing an enormous number of distinct antibodies.
established, the lymphocyte becomes activated, cloning              These concepts will be the building blocks of the models
itself. Clones with high capacity of recognizing a certain       presented in this work, which simulates the dynamics
antigen tend to proliferate. On the other hand, clones with      between paratopes and epitopes, and between antigens and
low recognizing capacity disappear and are replaced by           antibodies inside the organism along the evolution of a
others with higher efficiency [19, 27]. The analogy               species. This work was inspired by the ideas found in [3, 4,
between the clonal selection and the Darwinian natural           8, 10, 14–16, 21–25, 28–30].
selection [5] is clearly seen here.                                 Basically, in the above ideas which served as inspiration
   After recognizing an antigen by a B cell receptor, fol-       to the present work, the objective was ‘‘to develop models
lowed by a sequence of other events, a formation of plasma       directed at understanding the pattern recognition process of
cells clones responsible for the secretion of the same           two aspects of the IS, clonal selection and long term evo-
receptor in its soluble form takes place. This secreted          lution of genes.’’ In the works cited above most of the
receptor is the antibody and its function is to catch and bind   models work with binary strings evolved by genetic algo-
the antigen. This binding occurs between the paratope of         rithms (GAs) [10, 14, 16, 23, 28]. Other approaches
the antibody and the antigen’s correspondent epitope. A          involving artificial models and citations of many other
paratope that presents a strong bind within the epitope has a    Artificial immune systems (AIS) models can be found in
greater capacity of neutralizing the antigen [6, 7].             [2, 9, 20, 26, 36]. No comparison among the models of the
   An antibody is constituted by two equal heavy chains          present article has been made with the ones previously
and two light chains, as it can be seen in Fig. 1. The shape     cited, because the focus of each work was different.
of the molecule is similar to a Y. The base of the Y has            Evolutionary Computation has been chosen to imple-
parts of heavy chains and the arms are constituted by both       ment the models studied [33]. A coevolutionary genetic
chains. The antibody’s recognizing site is located at the end    algorithm (CGA) was used to form adaptive niching based
of each arm, and is known as V region. The antibody is           on the ideas of [8]. In that work, in contrast with fixed
antigen-specific, and to provide the organism with anti-          shared schemes, a niching formation strategy named
bodies able to recognize all the antigens, the antibodies’       coevolutionary shared niching (CSN) was proposed to
codifying genes suffer somatic recombinations (Fig. 2).          allow for the adaptation of the location and the radius of
   The variable portion of the light chain requires two          each niche . CSN was inspired by Tullock’s [35] economic
distinct DNA encoding segments. The V one encodes most           model of monopolistic competition where ‘‘businessmen’’
of the variable region. The remaining is encoded by a J
segment. In a non-activated B cell, the V and C regions
encoding DNA sequences are spatially apart from each
other. When B lymphocytes become mature, the somatic
recombination joins genes from segments V, J and C. The
C segment encodes the light chain constant portion of the
antibody. This mechanism is illustrated in Fig. 2.




                                                                 Fig. 2 Generation of the antibody’s chains given by somatic
Fig. 1 The antibody molecule. Adapted from [19]                  recombinations (adapted from [19])


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Evol. Intel. (2008) 1:133–144                                                                                              135


locate themselves among geographically distributed ‘‘cli-         2.1.1 Encoding
ents’’ so as to maximize their profit.
   Four models are described in Sects. 2–5, respectively,         In real biological systems, it is known that the constituting
which also present numerical experiments. The paper ends          regions of epitopes and paratopes are formed by complex
with Sect. 6 which discusses the results of our work. It is       chains of organic compounds. Nevertheless, in this artificial
important to make clear that this work does not focus on          model, epitopes and paratopes are represented by binary
theoretical immunology. The main objectives of the four           chains, following [8, 10]. Therefore, in the GA context [11,
models are to simulate the evolution of an AIS in order to        17], phenotypes and genotypes will be the same.
understand some aspects of biological IS development in
order to come up with methods and algorithms to solve             2.1.2 Initialization
real-world engineering problems.
   Given the great amount of experiments made in all the          The initialization of paratopes can be made entirely at
models with similar results, it was decided to show only the      random or, according to [10], by inserting some pre-defined
most important graphs containing the evolution of each            binary blocks in the chromosome.
model.
                                                                  2.1.3 Niche distribution
2 The first model
                                                                  The number of niches is always the same as the paratope’s
In the first model proposed, which represents a simplifi-           population size. In terms of the CSN, paratopes and epi-
cation of what happens in biological ISs, there is a group of     topes play the roles of the businessmen and clients,
paratopes that have to adapt through the generations, so          respectively. The distribution of epitopes among the niches
they can optimize the coverage of a fixed given group of           is determined by the smallest distance between them and
epitopes. The aim is to analyze the capability of adaptation      the paratopes. Each epitope is compared to a paratope, in
of the system in an environment full of aggressive ele-           order to establish which paratope is the closest one and,
ments, and its behavior due to pattern identification within       consequently, which niche the epitope will belong to. The
the epitopes structure as well. That is why the simulations       individuals in the jth niche are the epitopes that the jth
are initially performed with a number of paratopes smaller        paratope is more apt to neutralize among the current par-
than the number of epitopes.                                      atope population. The capability of a paratope to neutralize
   It is known that the antibodies are antigen-specific [19],      an epitope is measured by means of a distance computa-
meaning that it is assumed that there is just one paratope able   tion. Here, distance is understood as a function which
to bind itself to a particular epitope of the antigen molecule.   compares the epitope and paratope chromosomes, also
In this model, however, epitopes with slight structural dif-      known as matching function.
ferences can be inactivated by the same paratope.                    There are various types of matching functions [24],
                                                                  however, in this model, the one believed to be most faithful
2.1 The algorithm for the first model                              to biological systems was chosen. The chromosomes are
                                                                  compared bitwise, and the matching value is determined by
This sub-section will give details of the first model. The         the longest complementary chain between them, as it can
corresponding pseudo-code is shown in Algorithm 1. After          be seen in the following example.
the algorithm, each part of it is explained in details.
                                                                   Epitope: 0001111010101000011110
                                                                   Paratope: 1111011101010111111110
                                                                  MatchingValue ¼ 10
                                                                     The complementary chains represent the molecular bind
                                                                  between a paratope and an epitope. The objective is to
                                                                  reduce the distance between paratopes and epitopes along
                                                                  the evolution. The distance will be given by the formula in
                                                                  Eq. 1:
                                                                  Distance ¼ Epitope0 sChromosomeSize À MatchingValue
                                                                                                                    ð1Þ
                                                                    This distance presented by Eq. 1 is supposed to be
                                                                  minimized along the process of evolution.


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136                                                                                                 Evol. Intel. (2008) 1:133–144


2.1.4 Mutation

The genetic operator used was the classical mutation for
binary GAs, in which one bit is sorted and its value is
inverted. The mutation to an individual is retained only
when its fitness improves. This procedure makes the search
similar to Hill Climbing algorithms. It was chosen because
there was not an explicit objective function in the system
capable to determine gradients to drive the search. Thus, it
is the evaluation of a paratope mutation that guarantees a
bias to increase performance through the generations, and
allows the system to organize itself in the best way to
defend the organism.
                                                               Fig. 3 The evolution of the AIS considering populations of epitopes
                                                               and paratopes in different sizes
2.1.5 System’s general state evaluation

An important question for this model is how to determine       typical run with a mutation rate of 85%. The inefficiency
the efficacy of the generated system after a number of          limit was set to 10%.
generations, or, in other words, if it is capable to combat       As it can be seen in the graph of Fig. 3, at the start of the
the given epitopes.                                            evolution of the paratopes, there is no good performance of
   During the paratope’s population evolution, there will      the system in recognizing and neutralizing the epitopes.
be, at least, one minimum site of bind to all epitopes.        That is why the curve starts indicating a small number of
Nevertheless, it is prudent to say that weak binds are not     recognized epitopes (vertical axis). However, along the
able to produce efficient neutralizations, since they could     evolution course (horizontal axis), the artificial hypermu-
break when in contact with other molecules or under slight     tation mechanism enables paratopes to cover the epitopes
environmental variation.                                       population.
   Concerning this problem, a performance measure has             Another graph, presented in Fig. 4, shows the
been established to determine the efficiency rate in fighting    improvement of the fitness of the paratopes through the
aggressors. This parameter was named Inefficiency Limit,        generations. In this experiment, the number of epoches was
and its value corresponds to the minimum percentage of an      set to 200, chromosome size 65, paratopes population size
epitope that must be recognized by a paratope so that the      is 10, and epitopes population size is 300, which is the
latter can be considered inactive.                             maximum value to be reached by the paratopes population
                                                               as shown in the graph of Fig. 4.
2.1.6 Evaluation                                                  The results observed showed a great similarity to real
                                                               ISs. Those who were able to adapt to new pathogens
The evaluation is obtained by observing individually the
paratope; it is a self-organized system in which what is
expected is the individual action of each paratope leading
to an efficient global defense system.

2.2 Experiments

2.2.1 The first example

This first example shows the adaptation of the paratopes
according to a fixed epitopes population. It considers an
epitope population greater than the paratope population and
explores the capacity of the model in recognizing patterns
and grouping the epitopes into niches.
   Experiments have shown that mutation probabilities
ranging from 60 to 85% do not interfere with the evolution     Fig. 4 The evolution of the sum of the paratopes fitness the
of the paratopes. The results presented correspond to a        populations of epitopes and paratopes have different sizes


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                                                                      Fig. 7 An antigenic molecule and the correspondent binding
                                                                      antibodies


                                                                      3 The second model

                                                                      The first model was the simplest prototype elaborated in
Fig. 5 The evolution of the AIS considering populations of the same   this work and it presents some limitations. The main lim-
size                                                                  itation is that it broadens the specific antigenic restriction
                                                                      for each antibody. During the implementation and the
                                                                      analysis of this model, an upgrade of the first system was
survived and multiplied. In this model, one can simulate a            presented as the second version in which the behavioral
system inefficient in recognizing the epitopes by increasing           patterns would be more faithful to real ISs.
the inefficiency limit parameter.                                         It is known that molecules have to be large, rigid and
                                                                      chemically complex to be considered antigenic [34].
2.2.2 The second example                                              Pathogenic organisms—such as bacteria, anomalous cells
                                                                      or erythrocytes—can start up an immune response because
In this second example, shown in Fig. 5, paratopes and                their structure has a complex compound of various mole-
epitopes populations have the same size. Now the model                cules that alone are taken as antigens [1, 4].
is closer to the real biological systems. What is examined               As a result, a bacteria could be seen as an antigenic
here is the capacity of the system in neutralizing the                region with a multiple bind site for antibodies, for example.
given epitopes.The Inefficiency Limit was increased to                 Each site stands for a different antigen. After the study of
50%. Both epitope’s and paratope’s population have a                  these notions, it was possible to establish new parameters
size of 100, and chromosomes 25-bit long. Two hundred                 to improve the model.
epoches were performed. Another graph, presented in                      The new version does not deal with epitopes and para-
Fig. 6, shows the improvement of paratopes fitness along               topes, but antibodies and antigenic regions. This idea was
the evolution.                                                        adopted to make possible the implementation of binding
                                                                      sites of pathogenic molecules, where antibodies could
                                                                      match. Now the antigenic regions are represented by longer
                                                                      bit chains, and antibodies of shorter bit sequences that have
                                                                      to bind to antigen sub-chains. These sub-chains represent
                                                                      the antigenic determinants for the molecule.
                                                                         Figure 7 shows an example of the new model. Only one
                                                                      antigenic molecule was considered, and a possible con-
                                                                      figuration of antibodies to neutralize it is also shown in the
                                                                      bottom of the figure.
                                                                         In Fig. 7 four different antibodies were generated. They
                                                                      were all able to recognize and neutralize antigens within a
                                                                      molecule. The matching rate for antigenic determinant
                                                                      identification was set to 100%. The following sub-sections
                                                                      explain in detail how this new model was implemented.

                                                                      3.1 The algorithm for the second model

                                                                      The algorithm corresponding to the first model underwent
Fig. 6 The evolution of the sum of the paratopes fitness. The          some changes in order to accommodate the additional
populations of epitopes and paratopes have equal sizes                requirements, as shown in Algorithm 2.


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                                                               strategy similar to the one used in CSN [12] was adopted.
                                                               The algorithm accepts only mutations that generate dif-
                                                               ferent individuals from the ones that are already part of the
                                                               population. This difference is given by the Hamming dis-
                                                               tance, which must be greater than zero.

                                                               3.1.2 Evaluation

                                                               For each time the antibody equals the matching function to
                                                               a given antigen, the antibody’s fitness is increased by one
                                                               point. If it happens that the matching rate is bellow the
                                                               minimum value required to indicate a binding location, a
                                                               score lower than one is added to the antibody’s fitness. The
                                                               score value is found by dividing the matching rate by the
                                                               smallest chromosome size. This method is used to avoid
3.1.1 Niches distribution
                                                               loss in combinations that could potentially excel in future
                                                               generations.
In this new strategy a role reversal between antibodies and
the antigenic molecules occurs. The niche owner, or
‘‘businessman’’ in the monopolistic competition model are      3.1.3 System’s general state evaluation
now the antigenic molecules, and the antibodies are the
‘‘clients’’.                                                   In this second model, there is also the individual evaluation
   The decision to alter the original configurations emerged    for the antibodies. This leads the system to self-adjust in
because the new system has the ability to determine, to        order to increase its covering of the antigen group. Rele-
each antigenic molecule, a new group of binding antibod-       vant to the system, nevertheless, is not only the
ies. In the model, every antigenic determinant represents an   improvement to the antibodies’ fitness, but also the sys-
antigen and has a fixed part of the chromosome. All parts       tem’s capability to maximize the neutralization of any
have the same size, which is also the size of the antibody’s   antigen given. This characteristic is clearly derived from
chromosome.                                                    the improvement of the system.
   The assignment of an antibody to a specific niche occurs
when this antibody reaches a certain rate in the matching      3.2 Experiments
function when paired to some antigen in the molecule. It is
possible to notice a peculiar situation is derived from the    3.2.1 The first example
model’s evolution. There will be situations when an anti-
body will take part in more than one niche. This means that    This second model explores pattern recognition into the
some niches will intersect. In immunological theory, this is   antigenic molecules. The following graphs show the evo-
named cross reaction.                                          lution of two instances containing different numbers of
   Some of the initial difficulties in obtaining the expected   antibodies. The first example represents a model with a
behavior from the model derived from this particular fea-      small number of antibodies, whose mission is to find equal
ture. In some examples that had been run in an intermediate    building blocks into the antigens and maximizing the
model between the first model and the Algorithm 2, large        neutralization of the whole antigens population.
populations of antigenic molecules were used. This created        The graph in Fig. 8 shows the evolution of the system
various identical sub-chain gene patterns of chromosomes       producing antibodies able to adapt to the antigenic mol-
within the genotype. Consequently, the antibody popula-        ecules given. The vertical axis shows the antigenic
tion biased these more frequent sub-chains. At first, it        molecules reconized by the system. The horizontal axis
seemed natural, for it is believed the greater the antigen     are the epoches. The first example paratope’s population
number the more attention they draw from defense               size was set to 50, epitopes’ 300. The paratope’s chro-
mechanisms.                                                    mosome size was 8 and epitope’s, 64. All these numbers
   However, forming various identical antibodies within        of chromosome sizes, amount of epitopes and paratopes
the population was not the objective of this model. In the     have been empirically determined, after many experi-
second model, each antibody in the population represents       ments using other values. In the results of Fig. 8, not all
the whole group of antibodies secreted by a plasma cell        the epitopes have been recognized because of binary
clone. To solve the problem of identical antibodies, a         limitations.


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Evol. Intel. (2008) 1:133–144                                                                                                   139




                                                               Fig. 10 An example of a library individual after some generations

                                                               to observe how the coevolution would proceed during
                                                               the generations in terms of velocity, expansion of gene
                                                               libraries and robustness.

                                                               4.1 The libraries population’s GA

Fig. 8 The evolution of the AIS in the first example            In order to implement the system, each individual in this
                                                               first GA’s population represents a simplified library which
3.2.2 The second example                                       contains only three binary encoded segment groups V, D
                                                               and J. Initially, the libraries have only one segment of each
The second example, shown in Fig. 9 introduces a greater       group and their initialization is entirely randomly made.
number of antibodies and shows how this could improve          One example of an individual is shown in Fig. 10. The
the performance of the AIS. The paratopes’ population size     junction between one segment of each group forms the
was set to 100 and the epitopes’ to 200.                       genetic code for producing an antibody.
                                                                  Decoding an individual here means to produce all of its
                                                               potential antibodies repertoire. This is done by making
4 The third model                                              recombination between the individual library segments of
                                                               V, D and J kind, in this order, as shown in Fig. 11. During
The antibodies’V region task consists of recognizing the       the evaluation, this repertoire is contrasted to a binary
antigens. This region is encoded by libraries of gene seg-     chained antigens population.
ments. The V light chain requires three DNA segments from         The libraries’ recombination operator used was a
the types called V, J and C. The heavy chain is encoded by     crossover in which one of the segment groups V, D, or J, is
four segments, V, D, J and C. The somatic recombination        randomly chosen and exchanged between the parents, as
between these segments is one of the main lymphocytes—         shown in Fig. 12.
and therefore, antibodies—diversity generators.
   The third model simulates the coevolution between an
artificial species’ lymphocytes’ encoding genes library and
an antigens’ population. This simulation was implemented
using CGAs. The objective was to obtain a gene library
which produces antibodies that would recognize any
possible mutation in the antigens’ genes. It was also a goal

                                                               Fig. 11 Antibodies generation. The first antibody was created by the
                                                               junction of the first gene segment of V, followed by segments D and J.
                                                               The second one was created by the junction of the V’s second gene
                                                               segment with D and J




Fig. 9 The evolution of the AIS in the second example          Fig. 12 Crossover operator


                                                                                                                        123
140                                                                                                 Evol. Intel. (2008) 1:133–144


                                                                 certainly not be destroyed and keep being harmful. Fol-
                                                                 lowing these ideas, it was defined that the antigen
                                                                 individual would suffer mutations and its fitness would be
                                                                 increased as much as its capacity to remain unrecognized.
                                                                    A mutation in the antigen’s chromosome is made by
                                                                 randomly selecting and inverting a bit. If this mutation
                                                                 produces a better individual, the former chromosome is
                                                                 replaced by the new one. Otherwise, the operation is
Fig. 13 Mutation operators applied to the V group of genes       ignored. The fitness calculation is similar to the one done
                                                                 for libraries, which means that the value of fitness is given
   There are three kinds of mutation in the libraries’ GA.       by the matching function, given by Eq. 1. The difference is
After randomly selecting a segment group to mutate, the          that the antibodies have to maximize matching in the niche,
next step is to establish, probabilistically, the mutation       while antigens need to minimize it.
mechanism. The additive mutation introduces a new seg-              Algorithm 4 shows in detail the algorithm for the anti-
ment into the selected group. The subtractive one removes        gens evolution.
a randomly chosen segment, and the inversive mutation
randomly selects a segment and one of its bit to be inver-
ted. These mechanisms are illustrated in Fig. 13.
   The fitness of each library is given by its capacity of
producing an antibody potential repertoire capable of
maximizing the neutralization of the antigens population.
To neutralize an antigen, the antibody’s paratope needs to
bind an antigenic determinant in the pathogen’s molecule.
In the model, the antibody is constituted only by the par-
atope. The antigen can be larger than the antibody. Thus,
there might be more than one region in the antigenic
molecule where a set of antibodies could bind. An example
is shown in Fig. 7.
   The pseudo-code for the libraries’ GA is shown in
Algorithm 3.                                                     4.3 The main algorithm

                                                                 This section shows schematically how the whole system
                                                                 works. The main pseudo-code is presented in Algorithm 5.
                                                                 For each population GA, the components described in
                                                                 Sects. 4.1 and 4.2 were implemented. The number of the
                                                                 main algorithm epochs and generations for each population
                                                                 are parameters to be defined by the user.




4.2 The antigens population’s GA
                                                                 4.4 Experiments
An individual in the antigens’ population is represented by
a bit string. The GA operates in the population only by          4.4.1 The first example
making mutations on the individual’s chromosome. If the
mutation increases the antigen fitness, the change on the         In this first experiment, the parameters used for the libraries
genetic material is kept. Otherwise, it is reversed.             population GA were 120 generations per epoch, ten indi-
   The antigen fitness is given by its capacity of aggression     viduals in the population, elitism of one individual, 4 bits
inside the organism. If the pathogen is not identified, it will   per gene segment and 85% of probability of crossover and



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mutation. The probabilities of application assigned to the                                                                The Evolution of the Artificial Immune System

additive, subtractive, and inversive mutations were,                                                           140
respectively, 20, 10, and 70%. The group of segments V, D,
and J had the same chances of selection for mutation. The                                                      120




                                                                                         Recognized Antigens
genetic operators’ values have been adopted based in what                                                      100

is found in nature. The antigens GA used 400 generations,
                                                                                                                80
200 individuals, 64 bits per chromosome and 85% of
mutation probability. The number of recognized antigens                                                         60

along the generations is shown in the graphic of Fig. 14.
                                                                                                                40
   As it can be seen in the evolutive curve shown, at the
beginning of the evolution, the gene libraries are not yet                                                      20


robust enough to recognize new antigens produced by the                                                          0
                                                                                                                     0   1000   2000   3000   4000   5000   6000   7000   8000   9000   10000
mutation mechanisms. That is why there is first an increase                                                                                      Generations
of neutralization and then, when antigens starts to evolute,
this neutralization decreases. As the evolution of the arti-                            Fig. 15 The evolution of the AIS in the second experiment
ficial species proceeds, the library genes rapidly self-adjust
in order to have a minimum repertoire able to produce                                      This fourth model simulates tolerance by adding a new
receptors to identify and eliminate any given antigen.                                  population representing self. Now, the libraries’ population
                                                                                        has to evolve maximizing the coverage of the antigens
4.4.2 The second example                                                                population and minimizing the attack of self-molecules. To
                                                                                        implement this new requirement, a penalty for those indi-
In this second experiment the number of generations for the                             viduals that produce self-reactive antibodies is introduced.
libraries’ GA was reduced to 100. The other parameters had                              Such penalty is computed by dividing the antibodies’ fit-
the same values used in the previous example. The antigens’                             ness sum by the number of self-molecules attacked. The
GA used 200 generations, 150 individuals and 60% of                                     algorithms for this fourth model are presented in the fol-
mutation probability. The results are shown in Fig. 15. In                              lowing algorithms.
this example, as there is a smaller number of antigens, the                                The pseudo-code for the libraries’ GA is shown in
libraries’ stability is achieved in a shorter period of time.                           Algorithm 6.


5 The fourth model

The next step in this work was to consider the biological IS
tolerance characteristic. To be self-tolerant, an IS must
distinguish between foreign molecules and those that
belong to the organism, so that its cells and molecules will
not self-attack [31].

                                 The Evolution of the Artificial Immune System
                       200




                       150
 Recognized Antigens




                                                                                           The pseudo code for the antigen’s algorithms and main
                       100
                                                                                        algorithm is equal to the ones presented in model 3—
                                                                                        Algorithm 5 and 4.

                        50                                                              5.1 Experiments

                                                                                        5.1.1 The first example
                         0
                             0   1000    2000     3000    4000    5000    6000   7000
                                                   Generations
                                                                                        In the first experiment, the libraries’ GA used 600 gener-
Fig. 14 The evolution of the AIS in the first experiment                                 ations per epoch, ten individuals in the population and one


                                                                                                                                                                                 123
142                                                                                                                                                                           Evol. Intel. (2008) 1:133–144


individual as part of elitism. The other parameters assumed                                                                                        The Evolution of the IS Considering Self Molecules
                                                                                                                                         200
the same values used in the previous model, 4 bits per gene




                                                                                                        Recognized Antigenic Molecules
segment and 85% of probability of crossover and mutation.
The antigens’ GA used 1,500 generations per epoch, 100                                                                                   150




                                                                                                               without self harm
individuals with chromosomes of 120 bits and mutation
probability of 85%. The self-population had size 50 and its
                                                                                                                                         100
molecules were represented by chromosomes of 12 bits.
   The size of chromosomes in the antigens and self-pop-
ulations were set in different values because of the binary                                                                              50

strings limitations. Using an equal number of bits, there
could be problems such as very similar sequences of zeros
                                                                                                                                           0
and ones in individuals from self and antigens populations.                                                                                    0         5000        10000      15000       20000       25000
That would result in antibodies automatically matching self                                                                                                            Generations

when matching antigens.
                                                                                                        Fig. 17 The evolution of the AIS in the second experiment
   The results obtained with the first set of parameters can
be seen in Fig. 16. Here, results different from the other
model were obtained. Initially, the libraries evolved to                                                towards having strings in their genotype similar to self. In
cover the antigens, and although this evolution proceeded                                               other words, antigens have mimicked self.
slower, most pathogens were matched without self-harm.                                                     This fact showed the main model limitation: when
Nevertheless, by the time antigens mutated, libraries could                                             antigens became similar to self-molecules, there are no
not identify them anymore, not even considering all the rest                                            more antibodies’ effective defense mechanisms. This leads
of the evolution.                                                                                       to the conclusion that in real biological ISs this could also
                                                                                                        happen. Thus, there must be other protection means to
5.1.2 The second example                                                                                avoid self-similar antigens to invade an organism.
                                                                                                           In biological ISs this task is performed by T-cells,
Some parameter changes were made, in this second                                                        whose function, among others, is to detect anomalous cells,
example, in order to confirm the system’s behavior shown                                                 such as those that have suffered pathogenic invasions, or
in the previous case. For the libraries’ GA 1,000 genera-                                               tumoral cells. The experiment showed the importance of T-
tions per epoch were used. The antigens’ GA had 200                                                     cells inside the organism as another source of protection.
individuals also with chromosomes of 120 bits. The self-
population had the same parameters used in the previous
example. The results are shown in Fig. 17.                                                              6 Conclusions
   Once more, the libraries could not evolve towards
antigens neutralization. And specifically in this case, no                                               Understanding how ISs in mammals have evolved to their
antigen was recognized at the end of the evolution. The                                                 present configuration is challenging but it also may be the
explanation for this phenomena is that the antigens evolved                                             key to figure out more details of their mechanisms. This
                                                                                                        paper has proposed four binary encoded models describing
                                                                                                        some aspects of the evolution in an artificial IS with some
                                            The Evolution of the IS Considering Self Molecules
                                                                                                        characteristics similar to the real biological systems.
                                  100
                                                                                                           The first model has focused on the evolution of a para-
                                                                                                        tope’s population considering a fixed group of epitopes. The
 Recognized Antigenic Molecules




                                  80                                                                    objective of this first experiment was to simulate a hyper-
                                                                                                        mutation mechanism and observe how the system would
        without self harm




                                  60                                                                    self-adjust to cover the epitopes. This covering capacity is
                                                                                                        the measure of how well the system could protect an arti-
                                  40
                                                                                                        ficial specie along its evolution. The results of this first
                                                                                                        experiment showed that, at the beginning of the evolution,
                                                                                                        the paratopes available were not well adapted to the epi-
                                  20
                                                                                                        topes. However, as the evolution proceeded, the paratopes
                                                                                                        were becoming much more adapted to the environment
                                    0
                                        0       1000      2000       3000      4000    5000      6000   presented, being able to recognize almost all epitopes given.
                                                                 Generations
                                                                                                           The improvement of the first model produced a second
Fig. 16 The evolution of the AIS in the first experiment                                                 model with characteristics more similar to real ISs. Instead


123
Evol. Intel. (2008) 1:133–144                                                                                                            143


of paratopes and epitopes, the evolution involved a group             4. Cormack DH (1991) HAM histology (in Portuguese), 9 edn.
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