Prebiotic Aggregates (Tissues) Emerging from Reaction–Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension

Abstract

For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5.

Measuring habitat complexity and spatial heterogeneity in ecology

“…In between these integer values, complexity likely obeys a hump‐shaped (unimodal) relationship to , increasing at first and then decreasing. But there is no consensus on the precise value of at which complexity peaks (Flores, 2022; Gao et al, 2007; Kak, 2021; Palmer, 1992). Nevertheless, in many situations in ecology, values of have a small decimal component (e.g.…”

Configurations of Proto-Cell Aggregates with Anisotropy: Gravity Promotes Complexity in Theoretical Biology

“…That is, if there are multiple equivalent solutions A for a given |B o |, these solutions can be added together due to the particular linearity of Equation (1). In addition, from the expected growth of species A; condition [12] 2k…”

“…The following concepts [11] are adopted as a framework and used in the construction of a proto-tissue model in a finite spatial region [12]: a.…”

“…I emphasize the generation, not of an isolated cell, but of a structure comprising elementary proto-cells. This is the framework of so-called complex systems, and the concept of morphogenesis [ 9 , 10 , 11 , 12 ]. Meanwhile, the relevant conception of inheritance will be explicitly considered in the sense of viability through adaptation in open systems.…”

“…The following concepts [ 11 ] are adopted as a framework and used in the construction of a proto-tissue model in a finite spatial region [ 12 ]: Replication. Reactants interact to produce compound mainly from another chemical compound, substrate .…”