We consider that the nucleus of a cell can be a biological Data Terminal Equipment (DTE) which contains DNA molecules as an information source (i.e., the transmitter). DNA organizes genetic information into nucleotide blocks called genes. A gene is usually defined as a set of nucleotides that stores information that allows a protein or RNA (ribonucleic acid) to fulfill a biological function in some target organs [8]. Thus, for digital systems, the content of a gene includes information that directs it towards its receiver [1]. Addressing (or routing in digital systems) is also essential in biological systems because it allows the system to unequivocally identify the target organ to which the information will be transmitted for the completion of a biological function in the human body (which is beneficial in medical treatments that allow, for instance, the timely identification of tumor cells). The DNA content represents digital information, as it consists of four discrete values that denote the four types of nucleotides. A nucleotide is a monomer or subunit of nucleic acids (DNA or RNA) and is composed of a nitrogenous base, a chain of five sugars and a phosphate group. There are five nitrogen bases: Adenine (A), Thymine (T), Cytosine (C), Guanine (G), and Uracil (U).

At the beginning of transcription, an enzyme called RNA polymerase II (RNAP) recognizes a region in the DNA sequence known as the promoter, which contains information for the initiation of transcription. Next, RNAP merges nucleotides to form complementary sequences of messenger RNA (mRNA) into a single chain of biological information that is identical to that of DNA except for the replacement of thymine by uracil. Another element that is present in the DNA sequence is the so-called enhancer, which is responsible for regulating the amount of mRNAs produced and are sent to a biological receptor [9]. Digitally, the action performed by the enhancer can be considered to be a flow control mechanism, a mechanism used by the receiver to manage the amount of information that a transmitter communicates [2, 10]. At the end of transcription, the primary mRNA molecules are matured via the following modifications [11]: splicing, placement of a cap, and placement of a poly-A tail which can be considered as an error control mechanism in digital communication systems.

Once transcription ends, the genetic information should be transmitted from the DTE to the Digital Communication Equipment (DCE). In a conventional communication system, this connectivity takes place using a physical interface. In molecular systems, this connectivity occurs in the cytosol [1] From our perspective, the ribosomes and Endoplasmic Reticulum (ER) represent the DCE because these organelles provide a functional structure (or the appropriate format) to the genetic information so that it can travel via biological transmission and reach the receiver. The biological information is appropriately formatted during the process of genetic translation, in the form of chains of amino acids with functions inside the cell (autocrine system) or outside the cell (paracrine and endocrine systems). Thus, the biological DCE encodes information via translation by associating a specific input sequence (data in the mRNA) with a specific output sequence (amino acid chain). This process can be analogized to the codification of data in communication systems [1]. Subsequently, proteins are transmitted through an endoplasmic membrane.

We will briefly refer to protein-type hormones that are excreted by transmitting cells and are transported through the bloodstream to reach a target organ (endocrine system) to communicate between distant cells. This type of transport follows the physical laws of Fick and Brownian-type movement of particles for the transmission of fluids with drift. As in conventional communication systems, in the bloodstream, the information signal is also degraded because of the coverage distance of the transmission and the noise. This is due to the behavior of random-origin biological particles and unwanted chemical reactions among the molecules. For instance, Fig. (1) illustrates the particles P₁, P₂, and P₃, arriving at different times (i.e., in different order) from the transmitter to the receiver [12]. The communication problems, as mentioned earlier, can cause latency, jitter, increase losses, and also Inter-Symbol Interference (ISI).

Fig. (2) represents the propagation of molecules in a flow with drift [13, 14] that follows

Fig. (1). Transposition of biological information between the transmission and reception ends.

Fig. (2). Probability density function of the latency in a fluid medium for various fluid velocities v = {0,0.1,0.2,0.4}, D = 0.1 µm2/s, d = 4µm.

(1)

Where v ≥ 0 represents the drift velocity of the fluid, D is the diffusion coefficient of the molecule, and d is the distance from the transmitter to the receiver.

Based on the communicational parameters that denote the problems that can occur in a communication channel with noise, the Shannon theorem [7] is used to determine the maximum biological information transfer speed (capacity of a channel) as [15]

(2)

where I(X ; Y) represents the entropy of mutual information (MI) of X and Y. The information signals at the transmission and reception ends are denoted as X and Y, respectively. In Fig. (3), the result of the application of the Blahut-Arimoto algorithm to maximize the MI is shown. By this method, the biological transmitter sends a particle in each transmission slot. Also, in Fig. (3), mutual information (measured in bits) is displayed in relation to the diffusion constant and velocity or drift of the fluid.

In addition, the MI increases with the increase in velocity and reaches its maximum value at log₂(N), where N equals the number of transmission slots. If a transmitter does not send any molecule in any transmission slot, then the maximum value of MI will be log₂(N + 1). It is also notable that when the velocity values are high, the MI values do not depend on diffusion coefficient changes [15].

Fig. (3). Representation of the MI in relation to the velocity of drift and the diffusion coefficient [15].

Fig. (4). End-to-end communication system for gene expression.

In the molecular receiver, the information is processed through a structure formed by a ligand-receptor which acts as a transducer that decodes the received signal (acting as DCE). It is responsible for several biochemical reactions within the target cell or organ to fulfill a biological function in the body (acting as DTE) [16]. Thus, this biological transmission can be compared to that of the extreme-to-extreme type that is carried out in digital communication systems [1]. In Fig. (4), the proposed biological model is summarized, highlighting the contrasts with Shannon’s communication model.