Untangling Complex Systems, page 86
performances under their local conditions (see Figure 12.13).
21 Humans exploit the states of the inanimate matter to encode information, and specific machines (i.e., computers) to make computations.
22 A multicellular organism devoid of NIS exploits molecular signals to connect distinct cells.
23 Animals, micro-organisms, and plants that live in societies give rise to “Social Information Systems” (SISs). If the society has a hierarchical structure, we can distinguish the master, which takes the decisions, and the slaves which execute the orders. If the society does not have a hierarchical structure, the SIS grounds on the so-called “Swarm Intelligence”
(read paragraph 12.4.3).
24 In the deep sea, there are bioluminescent species that emit light useful for their spatial orientation.
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Untangling Complex Systems
BIS
IIS
NIS
B cells
T cells
Sensory proteins
Receptors
Sensory system
Intracellular
Intra- and inter–cellular
signaling network
Brain
signaling network
Genes
Molecular and
Effector system
cellular killers
FIGURE 12.12 Schematic structures of a Biomolecular Information System (BIS), an Immune Information
System (IIS), and a Neural Information System (NIS).
Blue and red light
Photosynthesis
Blue and red light
Photoperiodism
Optimize
Optimize
Photomorphogenesis
and phototropism
Feeds
Information for reproduction
and survival
Information for survival
FIGURE 12.13 The role of solar radiation for the fundamental activities of plants.
12.4.2.5.1 Photomorphogenesis
Photomorphogenesis refers to plant development. It is ruled by the photoreceptive protein
Phytochrome that absorbs either red (600–700 nm) or far-red (700–800 nm) light (Björn 2015). The
chromophore of Phytochrome is an open-chain tetrapyrrole that can switch between two configura-
tions within its apoprotein: one that absorbs the red ( R state) and the other the far-red ( FR state).
When the environmental light is wealthy of red, Phytochrome is switched from R to its FR state:
R red
→
FR [12.33]
Complex Systems
439
After process [12.33], a cascade of molecular signaling events occurs (Björn 2015) and a plant contin-
ues to grow steadily and quietly or, if it is still in the stage of a seed, it germinates. On the other hand,
when the environmental light is wealthy of far-red, Phytochrome switches from FR to its R state:
FR
far− red
→
R [12.34]
After process [12.34], another cascade of molecular signaling events occurs and, finally, a plant
accelerates its growth or, if it is in the stage of a seed, it does not germinate. These opposite responses
are linked to the clue a plant receives by absorbing either red or far-red light. Since the red is also
absorbed by chlorophyll, when the environmental light is wealthy in red, the plant infers that other
plants do not surround it, and it can germinate and grow without fearing competition. When the
environmental light is poor in red and wealthy in far-red, which is scattered and not absorbed by
other plants, it means there are many competitors, nearby. Therefore, if it is in the stage of a seed, it
does not germinate because the surrounding is highly competitive; if it is already a developed plant,
it accelerates its growth to become taller than its competitors and, hence, increase the survival prob-
ability by “eating” more sun.
12.4.2.5.2 Phototropism and Photoperiodism
Phototropism (Björn 2015) is the stimulation of an ensemble of processes that, ultimately, optimize
the photosynthetic efficiency of plants. Examples are:
• The movement of chloroplasts, which are the organelles devoted to the photosynthesis;
• Leaf orientation;
• The opening of stomata pores in the leaf epidermis, which regulates gaseous exchange
and, in particular, CO uptake;
2
• Heliotropism that is the power of tracking the movement of the sun.
All these processes are triggered by the blue light that is absorbed by the photoreceptive protein,
Phototropin, having a flavin mononucleotide as its chromophore. It is a molecular switch, like phy-
tochrome. The inactive form ( D) absorbs the blue and transforms into the active form ( L):
D blue
→
L [12.35]
L does not absorb the blue but lets it be absorbed by chlorophyll, which exploits it for photosyn-
thesis. At the same time, the L state, after a cascade of molecular signaling events, promotes the
processes that optimize the photosynthesis. Soon after the sunset, under the dark and at room tem-
perature, L transforms into D, spontaneously, and all the processes, optimizing photosynthesis, are
switched off.
L dark
→
D [12.36]
In this way, the plant rests, and Phototropin becomes ready to cover its role of detecting blue light,
the day after, at sunrise. Actually, plants measure the length of the day by another photoreceptor
protein, Cryptochrome, which is a flavoprotein sensitive to the blue. The acquisition of a circadian
rhythm is essential to rule both flowering time, a necessary trait for the optimization of pollination
and seed production, and dormancy, which is the temporary cessation of growth for the protection
of growing tissues in winter.
Of course, during their lifetimes, plants must deal not only with the light conditions but also with
variable temperatures, nutrient and water availability, as well as toxins and symbiotic, antagonistic
and commensal biota. Abiotic and biotic signals interact with the BIS of a plant. Due to the variety
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Untangling Complex Systems
of possible inputs, several sensory units operate in parallel and are “weighted” appropriately to reg-
ulate the “actuators.” The actuators are genes involved in cell division, cell expansion, and those that
affect the positioning, growth, and differentiation of primordia25 (Scheres and van der Putten 2017).
12.4.2.5.3 Unicel ular Organisms
Unicellular organisms, such as bacteria, algae, and protozoa trust in BISs like plants do. The main
difference is that micro-organisms can move thanks to their motor apparatus, cilia, or flagella.
Photoreceptor proteins allow micro-organisms to probe quality and quantity of the light present in
the environment. The light stimuli, after transduction and amplification, induce a modification of
the movement patterns and guide the cells into environmental niches where the illumination condi-
tions are the best for growth, survival, and/or development (Lenci 2008).
12.4.2.5.4 Animals
Animals that have NISs at their disposal can form images of their surroundings. This power derives
from the highly organized architecture of their visual sensory systems. If we focus just on the
human visual sensory system, we can state that its complex architecture allows us to see the shape,
color, and movement of objects, and recognize variable patterns. How is this possible? First of all,
we have organs specialized for vision: The eyes (Oyster 1999). The structure of an eye is similar to
that of a camera (see Figure 12.14): the cornea and crystalline lens play as the objective; the pupil and iris work as the diaphragm; the retina as the photosensitive film or CCD.
On the retina, there are four types of photoreceptor cells: one kind of rod (with 120 million of
replicas) and three types of cones (6 million altogether). The rods are abundant on the periphery of
the retina and work in the presence of scattered light (scotopic vision). The cones are concentrated in
the center of the retina (called fovea) and work in the presence of daylight (photopic vision). The rod
and the three types of cones differ in the spectral position of their lowest energy electronic absorp-
tion bands. These bands are all generated by seven transmembrane α-helices proteins having 11- cis
retinal as the chromophore. The first elementary step in human color vision is always the photo-
isomerization of the 11- cis retinal (see Chapter 7). The different spectral positions of the bands for the rod and the three cones are due to a distinct aminoacidic composition of the pocket embedding
the retinal chromophore. The three types of cones are labeled as “Blue,” “Green,” and “Red,” based
on the spectral position of their absorption bands (see Figure 12.15). They allow us to distinguish colors. How is it possible? The multiple information of a light stimulus, which is its modality ( M) or
spectral composition, intensity ( I ), spatial distribution ( I ( x, y, z)), and time evolution ( I ( x, y, z, t)), is M
M
M
Retina
Photoreceptor cells
Iris
Bipolar cells
Horizontal
Cornea
Fovea
cells
Pupil
Lens
Amacrine cells
Ganglion cells
Optic
Axons of ganglion cells: optic nerve
nerve
FIGURE 12.14 Schematic structure of a human eye (on the left) and retina (on the right).
25 In plants, leaf primordia are a group of cells that form new leaves near the top of the shoot. Flower primordia are the little buds that form at the end of stems, from which a flower develops.
Complex Systems
441
=
“Blue”
“Green”
“Red”
ership
of membeegrdeProbability of transition 400 450 500 550 600 650 700nm
Blue
Yellow
FIGURE 12.15 Absorption spectra of the Blue, Green, and Red photoreceptor proteins, and representation
of the degrees of membership of blue and yellow lights to the three Molecular Fuzzy sets.
encoded hierarchically. To rationalize the mechanism of encoding, we can invoke the theory of Fuzzy
sets (Gentili 2014a). A Fuzzy set, proposed by the electrical engineer Lotfi Zadeh (1965), is different
from a Boolean set because it breaks the Law of Excluded-Middle. In fact, an item may belong to a
Fuzzy set and its complement, at the same time, and with the same or different degree of membership.
The degree of membership ( μ) of an item to a Fuzzy set can be any real number included between
0 and 1:
0 ≤ µ ≤ 1 [12.37]
Let us make an example by considering the absorption bands of the three photoreceptor pro-
teins we have in the fovea. The absorption bands play like three Molecular Fuzzy sets. In fact,
when, for example, a blue light (having a wavelength of 425 nm) hits our fovea, it is absorbed
by both the Blue and the Green proteins, but not by the Red one. This behavior means that the
blue ray belongs to both the Blue and the Green absorption bands, but with different degrees:
µ ( Blue) > µ ( Green) > µ ( Red) = 0. On the other hand, a yellow light (having a wavelength of 570 nm) is absorbed by both the Green and the Red proteins. The yellow light belongs to both the
Green and the Red Molecular Fuzzy sets, but not to the Blue one. Moreover, it belongs more to
the Red protein rather than to the Green one: µ ( Red ) > µ ( Green) > µ ( Blue) = 0. These examples show that the information regarding the modality is encoded as degrees of membership of the light
stimulus to the Molecular Fuzzy sets. In other words, the modality is encoded as Fuzzy Information
at the Molecular Level (µ ML ).
The intensity of a light stimulus determines the number of retinal molecules that photo-isomerize
within a specific cone and per unit of time. Therefore, the information regarding the intensity is
encoded as degrees of membership of the light stimulus to the cones, which work as Cellular Fuzzy
sets. The intensity is encoded as Fuzzy Information at the Cellular Level (µ CL ). The information
regarding the spatial distribution I ( x, y, z) is encoded as degrees of membership of the light stimu-M
lus to the array of Cellular Fuzzy sets, covering the retina. In other words, the spatial distribution of
the light stimulus is encoded as Fuzzy information at the Tissue Level (µ TL ). The overall informa-
tion of a light stimulus is a matrix of data. The shape of the matrix reproduces the distribution of
cones on the fovea (assumed to lay on the x, y plane). Each term of the matrix, µ
( )
x
, is given by:
i , y
λ
i
−
(ε C )( C ) L
l
Cl
Φ
0
(1 10
)
C I
−
l
,λ
µ
( ) (
)
[12.38]
x
= (
)× (
)
=
i , y
λ
µ
i
ML
µ CL xi, yi
M
MAX
(
)
c
n t
→
/ t
∆
xi, yi
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Untangling Complex Systems
In [12.38], I 0,λ is the intensity of the incident light having wavelength λ. Φ C is the quantum yield l
for the photo-isomerization of retinal within cone C . ε and C are the absorption coefficient
l
Cl
cl
and concentration of the photo-receptor protein contained in cone C , respectively. L is the length
l
of the photosensitive part of the same cone, and ( nMAX )
c t
→
/ t
∆ is the maximum number of photo-
isomerization that can occur per unit time within C . l
The information of the light stimulus collected by the array of photoreceptor cells is not relayed
to the brain as such, but it is processed by an ensemble of neurons that is present in the retina. There
are bipolar and horizontal cells connected directly to rods and cones. Then, there are ganglion cells
joined to bipolar cells, and amacrine cells allowing the interconnection among bipolar and ganglion
cells that are far apart. The axons of ganglion cells form the optic nerve that relays the optical
signals to the visual cortex of the brain (see Figure 12.14). Each bipolar cell is connected directly to a number of photoreceptor cells located roughly opposite it. This number ranges from one photoreceptor at the center of the fovea to thousands in the periphery of the retina. In addition to these
direct vertical connections, each bipolar cell receives some of its afferences from horizontal cells.
The horizontal cells guarantee the connection of a bipolar cell to a set of more distant photorecep-
tors. All the photoreceptors connected to a bipolar cell define its receptive field that has a circular
shape. Since each cone and rod may be connected to more than one bipolar cell, the receptive fields
of bipolar cells are Fuzzy sets. A bipolar cell integrates the signals coming from different photore-
ceptor cells. Its final output depends on the activation pattern of the photosensitive cells belonging
to its receptive field. Light shining on the center of a bipolar cell’s receptive field and light shining
on the surround produce opposite changes in the cell’s membrane potential. The purpose of Bipolar
Fuzzy sets is to improve the contrast and definition of the visual stimulus. A further increase of con-
trast is achieved by the ganglion and amacrine cells. Each ganglion cell is connected directly to a
number of bipolar cells located roughly opposite to it. In addition, each ganglion cell receives some
of its afferences from amacrine cells. The amacrine cells guarantee the connection among distant
bipolar and ganglion cells. All the photoreceptor cells indirectly connected to a ganglion cell define
its receptive field that has a circular shape. The receptive fields of ganglion cells are Fuzzy sets that
include more photosensitive cells than the Bipolar Fuzzy sets. In fact, each eye has about 126 mil-
lion of photosensitive cells and just 1 million of ganglion cells. It is clear that one photoreceptor
cell influences the activity of hundreds or thousands of Ganglion Fuzzy sets. The center-surround
structure of the receptive fields of bipolar cells is transmitted to the ganglion cells. The accentua-
tion of contrasts by the center-surround receptive fields of the bipolar cells is thereby preserved and
passed on to the ganglion cells. The presence of overlapping receptive fields (like overlapping Fuzzy
sets) allows processing the information of a light stimulus in parallel and increasing the acuity by
highlighting the contrasts in space and time. For example, in the retinal ganglion cells, three chan-
nels convey the information about colors from the eye to the visual cortex (Gegenfurtner 2003). In
