The Information Encoded in Structures: Theory and Application to Molecular Cybernetics

Abstract

Theoretical frames for analyzing information in biological and molecular multicomponent structures are proposed. The mathematical foundations of the proposal are presented. Both the information encoded in structures is defined and the method of calculating the amount of this information is introduced. The proposed approach is applied to the operation of a molecular multicomponent machine.

The concept of structural information and possible applications

“…Studies on information often lead to the conclusion that the concept of information is indeed related to the concept of structure (Burgin, 2011;Bielecki, 2015;Bielecki and Schmittel, 2022;Tao et al, 2021). The concept of information discussed in this article falls within this line of research.…”

“…The very idea presented in this section was outlined in (Bielecki, 2015) and presented in (Bielecki and Schmittel, 2022) in which structural information was introduced. In this section the concept is clarified, refined in detail, discussed and complemented with definitions of two sorts of existential information.…”

“…(x,y) 𝜖 E if xℛy. On a given set a few various relations can be specified, among others labelling that has a specific meaning in this context (for details see Bielecki and Schmittel, 2022). The above idea concerning the fundamental relationship between the relation on a set and the graph has a classical rank today (Carnap, 1928).…”

“….∩𝑌 𝑘𝑚 , where 𝑌 𝑘𝑖 denotes the k i -th equivalence class in the i-th relation, generate the new partition of X and formula (2) is applied to this new partition. Let us note that supplementing the approach presented in (Bielecki and Schmittel, 2022) with node existential information is necessary, because otherwise sets with a different number of elements on which there would be no relation would generate the same amount of information, in both cases equal to zero, which would be counterintuitive.…”

Towards Autonomous Materials–Challenges in Chemical Communication

“…Concatenation of multiple such entities and leveraging energy transfer allows building more sophisticated integrating units. Molecular machines, in the form of nano-switches, can provide an excellent tool for concatenation of logic function and hence molecular logics, as demonstrated by Schmittel [72] and others. In one example, [73] a nano-cage is responsive to three inputs: without input, the system is catalytically active; upon addition of Zn 2 + , Cu + , or H + catalysis shuts down; only when all three inputs are added the system shows fluorescence output.…”