Is it possible to engraft TCS systems into SC, for neural network-like operations? TCS systems mediate bacteria response to a wide range of signals and stimuli, such as nutrients, cellular redox state, pH, light, temperature, dissolved gases, quorum signals, hormones, osmolarity, antibiotics, etc. (Laub and Goulian 2007; Stock et al., 2000). Each TCS system consists of three elements (i.e., the three neuron-like elements): a sensor (histidine kinase) (S), a response regulator (R), and a gene (G) (Figure 1B). The sensor, which is a transmembrane protein, detects an environmental stimulus by its N-terminal domain, triggering the (auto)phosphorylation of a histidine residue in its kinase domain at the expenses of cellular ATP. In turn, the phosphorylated sensor reacts with its cognate response regulator, transferring the phosphate group to an aspartate residue of the regulator (phosphotransfer reaction). The typical final step is the control of gene expression by the phosphorylated response regulator, or—more in general—the control of cell physiology. Such systems have received many attentions in recent years and many topologies (connectivities) are known. We are interested, for the moment, to show that a minimal neural network based on TCS systems can be implemented in SCs. At this aim, a possible design could be based either on 1) TCS sets that are per se branched (e.g., one-to-many and many-to-one systems), such as the sporulation phosphorelay of Bacillus subtilis and the M. tuberculosis hypoxia sensing (Agrawal et al., 2016), or 2) TCS sets designed ad hoc, by rewiring TCS or enhancing the cross-talk in otherwise orthogonal TCS systems.

Engineering connectivity in TCS systems is considered within the experimental reach. Recent reviews are the good starting point for an up-to-date discussion about the technical possibilities and strategies (Laub and Goulian, 2007; Capra and Laub, 2012). For example, the substrate specificity of S can be reprogrammed by mutating as few as three residues (Skerker et al., 2008), and similar achievements have been obtained by mutating response regulators (Capra et al., 2010; Bell et al., 2010). Examples based on directed evolution are available (Siryaporn et al., 2010). The use of chimeric molecules (Wang et al., 2013) is encouraged by the modular structure of response regulators. In addition, downstream information flow can be engineered by a proper swapping of the response regulator DNA-binding domains (Schmidle et al., 2018), or by constructing proper promoters-ORFs (Open Reading Frames) combination.

Promoting cross-talk is also possible as summarized by another recent review (Agrawal et al., 2016) proposing different mechanisms, based on S/S or R/R heteromerization, on non-cognate S/R phosphorylation, on coregulation of the same gene by two different R, or on introducing auxiliary proteins that favour cross-talk. Another possibility relies on the simultaneous presence of wild-type and mutant S (and/or R), in order to display different kinetic preference toward their cognate elements. As mentioned, knowledge about TCS has grown considerably since the Hellingwerf et al. (1995) report. The issue of kinetic preference of an S for its cognate R could be somehow tuned or compensated by an appropriate design (easily realized in SCs, much less in vivo), which relies on the altered concentration of the various components or on kinetic counteractions (compensations) based on downhill processes (e.g., gene transcription, playing with concentrations of DNA or RNA polymerases; or at the level of mRNA availability).

The goal of implementing a chemical neural network inside SCs somehow mirrors its function in vivo, i.e., the integration of different signals into a gene expression pattern in specific manner, via convergent and divergent signaling that characterizes the neural networks. This will be considered as the first desired outcome, but a far-looking goal will be instead aimed at self-regulatory dynamics, possibly resulting in compensatory/adaptive/plastic dynamics. This could be achieved if the products of gene expression are elements of the phospho-neural network itself or effectors that change its behavior (so to achieve a sort of closed causal loop).

As mentioned, implanting a chemical neural network in current SCs will be technically challenging. The frontier components, i.e., the sensors S are integral membrane proteins, and thus their embedment in the SC membrane is not at all trivial, as it must face several issues like the optimal lipid composition of SC membrane (in order to favour their functionality), as well as their orientation. Membrane proteins can be embedded in SC membranes by reconstitution. Previous reports show that sensors of TCS systems have been successfully reconstituted in liposomes. For example, MtrB is involved in the osmostress response of Corynebacterium glutamicum and it has been reconstituted in functional way, by employing liposomes made of E. coli phospholipids (Möker et al., 2007). Similarly, PhoQ Mg²⁺-sensor from Salmonella typhimurium has been reconstituted in liposomes (Sanowar et al., 2005). CpxA, the sensor of an E. coli TCS that detects envelop perturbation and it is also involved in biofilm formation, has been reconstituted in E. coli phospholipid nanodiscs (Hörnschemeyer et al., 2016). In all cases, the functionality of TCS systems was positively assessed, carrying out the phosphorylation pathway in vitro. Therefore, current knowledge could be employed as a guidance to 1) select systems that have been proved to function in liposomes; 2) reason about the best strategy for practical implementation of somehow similar “promising” systems. Alternatively, it could be attempted the direct in situ synthesis-and-insertion strategy of membrane proteins in SC membrane, from inside—typical of bottom-up autopoietic constructions (Kuruma et al., 2009; Altamura et al., 2017; Amati et al., 2020). Combinations of these approaches should be taken into consideration, recalling, however, that either detergent-based reconstitution either ribosomal synthesis-and-insertion require a careful design of the lipid composition of SC membrane, that must fulfil some requirements (form stable vesicles, be compatible with encapsulation procedure, allow the correct protein folding, do not interfere with protein synthesis and other intra-SC processes). Finally, the in situ synthesis of sensors and response regulators that require post-translational modifications can represent a further obstacle.

Despite these potential difficulties, we believe that implanting “minimal” phospho-neural networks in SCs is experimentally accessible, and that such plan would correspond to a major advancement in the field because it significantly adds to SC technology, especially from the viewpoint of developing artificial cognitive systems. Moreover, it contributes to merging SB and AI in a novel and potentially fruitful manner.

To complete the discussion, let us make a further step in the direction of chemical embodiment, by commenting on how chemical neural network could be modeled. We reasoned that in order to keep into account the real chemical nature of the neural network elements, which are proteins and thus can display conformational diversity, one needs to move from dichotomic two-state (yes/no) logic, as specified by sentences like “the sensor (or the response regulator) is/is not activated”, to the continuum case (gray-scale), typical of fuzzy logic. Thus, we further expect that intra-SC chemical neural network could become a useful study case of fuzzy logic application to complex chemical systems, and consequently allowing accurate modeling, insightful conclusions, and the departure from idealized binary logic.

We have emphasized that S and R elements of two different TCS systems can be specific or cross-talk (Agrawal et al., 2016), but, by the same reasoning, it is also possible that a single input signal can activate (at different degree) two similar sensors (e.g., nitrate activate, in E. coli, the two sensors NarX and NarQ (Noriega et al., 2010)). The schemes shown in Figures 1C,D describes both specificity and cross-talk. Note that it represents just a simple example of the neural network-like architectures we propose for SCs.

Firstly, it should be specified how parameters that are typically employed in neural networks are related to well-known physicochemical constants. Referring to Figures 1C,D, for instance, the degrees of membership x ₁ and x ₂ are related to the association constants of the chemical inputs to the two sensor proteins, S₁ and S₂; the weight coefficients w _ij are related to the kinetic constants (k _cat, K _M) of the phosphorylation reactions; the weight coefficients u _ij are related to the association constants of the phosphorylated R to the DNA. Examples of neural networks that map to chemical reactions have been reported, based on fundamental chemical laws (e.g., mass action, Arrhenius law) (Ji and Deng, 2021). The neural network “activation functions”, which is often a key parameter for the properly functioning of neural networks, should be based on physicochemical laws when referring to neural networks in the chemical domain. It would refer, therefore, to hyperbolic or sigmoidal isothermal binding curves, or to Michaelis-Menten profiles. Smooth analog input-output relationships are the most appropriate functions for processing the infinite-valued fuzzy logic. On the other hand, steep sigmoid functions are adequate for processing discrete logics, as it is Boolean binary logic (Gentili, 2011). The necessity of realistic modeling of chemical neural networks generates a set of constraints with respect to their operations and performance. Thus, what a chemical neural network can (and cannot) do, when compared to artificial neural network, represents one of the open questions that need to be addressed in future.

A fuzzy logic perspective starts from the consideration that each sensor (both S₁ and S₂) exists, in general, as a collection of conformers (Kenakin, 2011). Such conformational pluri-states confer every sensor the power of being sensitive to more than one input. However, distinct sensors react differently to different inputs. From this point of view, each sensor kinase behaves as a fuzzy set (Gentili 2014, 2018). Figure 1C shows that S₁ and S₂, being two molecular fuzzy sets, granulate the space defined by the chemical inputs. Distinct chemical inputs belong to the two molecular fuzzy sets at two different degrees. As an example, the figure shows that the input, represented as a chemical species X, belongs to both S₁ and S₂, but with two distinct degrees, which are x ₁ and x ₂. Each degree of membership x _i (i = 1 or 2) is proportional to the interaction strength between the input X and S _i . The combination of the two-degree-of-membership values, x ₁ and x ₂, is transduced into a peculiar set of values for the neural network weights shown in Figure 1D. We have cross-talk whenever both degrees of membership, x ₁ and x ₂, are not null. Then, it might also be that: w 12 ≠ 0   and / or   w 21 ≠ 0 u 12 ≠ 0   and / or   u 21 ≠ 0 The vector of network weight coefficients (w ₁₁, w ₁₂, w ₂₁, w ₂₂, u ₁₁, u ₁₂, u ₂₁, u ₂₂) is a function of the degrees of membership of the input to the two molecular fuzzy sets, which are the sensor proteins (i.e., S₁ and S₂): ( w 11 ,   w 12 ,   w 21 ,   w 22 , u 11 ,   u 12 ,   u 21 ,   u 22 ) = f ( x 1 ,   x 2 ) Specificity occurs when either ( x 2   =   0 )   ∧   ( w 12   =   0 )   ∧   ( u 12   =   0 ) or when ( x 1   =   0 )   ∧   ( w 21   =   0 )   ∧   ( u 21   =   0 )

It is worthwhile noticing that even the response regulators R and the genes G exist as collections of conformers. Therefore, they can exhibit an ensemble of reactivities, one for each conformer. It means that even R and G are fuzzy sets, and the network weight coefficients, w _ij and u _ij (i, j = 1 or 2), can assume—potentially—as many values as the number of reactive conformers. Clearly, the TCS systems are examples of chemical fuzzy neural networks. The possibility of processing fuzzy logic at the molecular level will simulate, in minimal way, some elementary yet fundamental features of biological intelligence (common to all organisms, from bacteria to human) to SCs such as that of making decisions in an environment of uncertainty, partiality and relativity of truth (Zadeh, 1973; Gentili, 2021) and that of recognizing variable patterns. In other words, SCs will become able to face complex scenarios and quickly adapt to an ever-changing environment.