# The Fuzziness of the Molecular World and Its Perspectives

## Abstract

**:**

## 1. Introduction

^{26}m far apart from us. At the same time, we can detect subatomic particles that have radii of the order of 10

^{−15}m. We can record microscopic phenomena that occur in 10

^{−18}s, but we can also retrieve traces of cosmic events happened billions of years ago. Our technology allows us to send robots to other planets of our solar system (e.g., the NASA Spirit rover on Mars), manipulate atoms and interfere with the expression of genes in living beings. Despite many efforts, there are still challenges that must be won. For instance, (I) we cannot predict catastrophic events on Earth (such as earthquakes and volcanic eruptions); (II) we strive to avoid the climate change; (III) we would like to exploit the energy and food resources without deteriorating the natural ecosystems and their biodiversity; (IV) there are diseases that are still incurable; (V) we would like to eradicate the poverty in the world; (VI) we make efforts to avoid or at least predict both economic and political crisis. Whenever we try to address such challenges, we experience frustrating insurmountable obstacles. Why? Because whenever we cope with one of them, we deal with a complex system. A complex system is one whose science is unable to give a complete and accurate description. In other words, scientists find difficulties in rationalizing and predicting the behaviors of complex systems. Examples of complex systems are the geology and the climate of the Earth; the ecosystems; each living being, in particular humans, giving rise to economic and social organizations, which are other examples of complex systems. The description of complex systems requires the collection, manipulation, and storage of big data [1], and the solution of problems of computational complexity. The description of complex systems from their ultimate constituents, i.e., atoms, is beyond our reach since the computational cost grows exponentially with the number of particles [2]. Moreover, many complex systems exhibit variable patterns. These variable patterns are objects (both inanimate and animate) or events whose recognition is made difficult by their multiple features, variability, and extreme sensitivity on the context. We still lack universally valid and effective algorithms for recognizing variable patterns [3]. Therefore, the obvious question is: How can we try to tackle the challenges regarding complex systems which involve issues of computational complexity? There are two principal strategies [4,5]. One consists in improving current electronic computers to make them faster and faster, and with increasingly large memory space. The other strategy is the interdisciplinary research line of natural computing. Researchers working on natural computing draw inspiration from Nature to propose: (I) new algorithms, (II) new materials and architecture for computing, and (III) new models to interpret complex systems. The sources of inspiration are the natural information systems, such as (a) the cells (i.e., the biomolecular information systems or BIS), (b) the nervous system (i.e., the neural information systems or NIS), (c) the immune system (i.e., the immune information systems or IIS), and (d) the societies (i.e., the societal information systems or SIS). Alternatively, we may exploit any causal event, involving inanimate matter, to make computation. In fact, in a causal event, the causes are the inputs and the effects are the outputs of a computation whose algorithm is defined by the laws governing the transformation (see Figure 1).

## 2. Some Features of Fuzzy Logic

_{1}and S

_{2}can be ${\mu}_{{S}_{1}\cup {S}_{2}}=\mathrm{max}\left[{\mu}_{{S}_{1}},{\mu}_{{S}_{2}}\right]$ or ${\mu}_{{S}_{1}\cup {S}_{2}}={\mu}_{{S}_{1}}+{\mu}_{{S}_{2}}-{\mu}_{{S}_{1}}\times {\mu}_{{S}_{2}}$); NOT corresponds to the complement (e.g., the membership function for the Fuzzy complement of S is ${\mu}_{\overline{S}}=1-{\mu}_{s}$). Fuzzy rules may be provided by experts or can be extracted from numerical data. After the granulation, the graduation of all the input and output variables, and the formulation of the fuzzy rules, we have a FLS that is a predictive tool or a decision support system for the particular phenomenon it describes. The way an FLS works is schematically depicted through an example in Figure 3.

## 3. Fuzzy Logic and the Human Nervous System

## 4. The Methodologies to Implement Fuzzy Sets and Process Fuzzy Logic at the Molecular Level

#### 4.1. The “Fuzzy Parallelism” Approach

_{i}, are assumed to be input fuzzy sets. Second, the absorption bands of the colored forms, B

_{i}, are assumed to be output fuzzy sets. Third, the algorithm expressing the degree of membership of the UV radiation, having intensity ${I}_{0}\left({\lambda}_{irr}\right)$ at the wavelength ${\lambda}_{irr}$, to the absorption band of the A

_{i}compound is:

_{i}, ${\epsilon}_{{A}_{i}}$ is the absorption coefficient at ${}_{irr}$ for the A

_{i}photochromic species, and ${C}_{0,i}$ is its analytical concentration. Finally, the equation expressing the activation of the B

_{i}output fuzzy sets is:

_{i}. Each absorption spectrum recorded at the photo-stationary state will be the sum of as many terms represented by equation (3) as there are photochromic components within the BIPFUL system. The BIPFUL systems that have been devised are made of naphthopyrans and spiroxazines, and they allow to discriminate the three regions of the UV spectrum, i.e., UV-A, UV-A, UV-B, and UV-C.

#### 4.2. “Conformational Fuzziness”

#### 4.3. “Quantum Fuzziness”

^{n}accessible states, simultaneously. If we make an operation on this system, we manipulate 2

^{n}states, at the same time. Therefore, it is evident the alluring computational power of quantum logic. However, the main difficulty is to avoid the decoherence of the superimposed quantum states, which can be induced by deleterious interactions with the surrounding environment [46]. The decoherence induces the collapse of a qubit in one of its two originally accessible states, either $|0\rangle $ or $|1\rangle $, with probabilities ${\left|a\right|}^{2}$ and ${\left|b\right|}^{2}$, respectively. Whenever the decoherence is unavoidable, the single particles can be used to process discrete logics, i.e., binary or multi-valued crisp logics [47,48]. Of course, specific microscopic techniques, reaching the atomic resolution, are needed to carry out the computations. Alternatively, we may think of making computations by exploiting large assemblies of particles, e.g., molecules. Vast collections of molecules (amounting to the order of the Avogadro’s number) appear as bulky materials. The inputs and outputs for making computations become macroscopic variables that can change in a continuous manner. The relations establishing between the inputs and the outputs can be either steep or smooth. Steep, sigmoid functions are suitable to implement discrete logics, whereas both linear and nonlinear smooth functions are suitable to build fuzzy logic systems [49]. Some fuzzy logic gates and operations have been implemented by the hybridization reaction of DNA [50,51] and the supramolecular interactions between carbohydrates and proteins [52]. Other fuzzy logic systems have been built by exploiting the dependence of the fluorescence quantum yield on physical and chemical inputs. One example is the dependence of the fluorescence of 6(5H)-phenanthridinone (see Figure 10A) on the hydrogen bonding donation ability of the solvent (HBD) and the temperature [53]. Another example is given by tryptophan, both as isolated molecule and bonded to the serum albumin, whose fluorescence depends on the temperature and the amount of the quencher flindersine (see Figure 10B) [54]. A further example is a ruthenium complex, whose fluorescence depends on Fe

^{2+}and F

^{−}(see Figure 10C) [55]. A final example is the fluorescence of europium bound to a metal-organic framework, which depends on metal cations, such as Hg

^{2+}and Ag

^{+}(see Figure 10D) [56]. The emission of light is a preferable output because it bridges the gap between the microscopic and the macroscopic world. A multi-responsive chromogenic compound, belonging to the class of spirooxazine, has been used for the implementation of the all fundamental fuzzy logic gates, AND, OR, and NOT [57]. The protons, Cu

^{2+}, and Al

^{3+}ions were used as inputs, and the color coordinates (R, G, B) or the colorability [41] of the chromogenic compound as outputs. Then, other platforms have been proposed. For example, a multi-state tantalum oxide memristive device [58] and an anthraquinone-modified titanium dioxide electrode [59]. Even, the Belousov-Zhabotinsky reaction, carried out in oscillatory regime and in an open system [60], allows to implement all the fundamental fuzzy logic gates by using bromide and silver ions as chemical inputs and the period of the oscillations as outputs. Finally, the “hydrodynamic photochemical oscillator”, which is a thermally reversible photochromic compound combined with the convective motion of the solvent, is suitable to implement fuzzy logic systems when it works in chaotic regime [61]. All these examples show that fuzzy logic can be processed not only by conventional electronic circuits but also by unconventional chemical systems exhibiting analog input-output relationships in either the liquid or the solid phase.

## 5. Perspectives of the Fuzziness of the Molecular World

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The contribution of the natural computing in coping with the challenges of the computational and natural complexity.

**Figure 2.**Shapes of the membership functions (μ) for a generic variable x: the case of a classical Boolean set in

**A**; examples of fuzzy sets with sigmoidal, triangular, trapezoidal, and Gaussian shapes are shown in

**B**,

**C**,

**D**, and

**E**plots, respectively.

**Figure 3.**The flow of information in a fuzzy logic system where AND, OR and the implication have been implemented through the minimum, the maximum, and the minimum operators, respectively.

**Figure 4.**An example of type-2 fuzzy set. The original type-1 fuzzy set is the dashed triangular set. The lower (LB) and upper (UB) bounds define the footprint of uncertainty. The plot on the left shows the trend of the secondary membership (w) when $x=x\prime $

**Figure 5.**Absorption spectra of the “Blue”, “Green”, and “Red” photoreceptors that partition the visible spectral region in three fuzzy sets. Beams having different colors belong to the three molecular Fuzzy sets at different degrees. The degrees of membership of one pure green and one pure red beam to three Fuzzy sets are shown (see the arrows).

**Figure 6.**Scheme of the action of a sensory subsystem made of three principal elements described as three collections of fuzzy sets. First, the sensory cellular Fuzzy sets (

**A**) that encode the information of a signal as graded potentials. Second, the afferent neurons (

**B**) whose receptive fields are fuzzy sets: they encode the information as firing rates of the action potential trains. Third, the cortical areas (

**C**) that are partitioned in different dynamic regimes giving rise to an infrastructure of fuzzy sets encoding distinct syntactic and semantic attributes of the original signals.

**Figure 9.**Just of a few of all the possible conformers of a merocyanine (MC

_{i}) produced by irradiation of a spirooxazine (SpO).

**Figure 10.**Dependence of the fluorescence quantum yield of 6(5H)-phenanthridinone (

**A**), tryptophan (

**B**), a ruthenium complex (

**C**), and europium bounded to a metal-organic framework (

**D**) on physical and chemical inputs.

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Gentili, P.L.
The Fuzziness of the Molecular World and Its Perspectives. *Molecules* **2018**, *23*, 2074.
https://doi.org/10.3390/molecules23082074

**AMA Style**

Gentili PL.
The Fuzziness of the Molecular World and Its Perspectives. *Molecules*. 2018; 23(8):2074.
https://doi.org/10.3390/molecules23082074

**Chicago/Turabian Style**

Gentili, Pier Luigi.
2018. "The Fuzziness of the Molecular World and Its Perspectives" *Molecules* 23, no. 8: 2074.
https://doi.org/10.3390/molecules23082074