On the Robust Power of Morphogenetic Systems for Time Bounded Computation

A Self-Controlled and Self-Healing Model of Bacterial Cells

“…In most cases, the missing part can be re-assembled as it did before, even if the sequence of steps may be different (due to the nondeterministic nature of M 0 ), and the new mature individual will bear only small differences compared to the individual before the injury, while keeping the original characteristics of the (uninjured) original M 0 . This property was verified quantitatively in [18], where results of a number of simulations on Cytos with injuries to the system M 0 were described. Interestingly, a certain number of injuries to the cytoskeleton elements led to a small increase of the survival ratio, but the system eventually collapsed when the number of injuries exceeded a critical threshold.…”

“…On the other hand, general properties of self-healing for arbitrary M systems can be established, as illustrated by the following proposition strengthening a result in [18]. Proposition 1.…”

“…This is in recognition of the important role that shape and physical location play in ordinary biology, usually not explicitly factored in most kinds of biological models. To avoid misunderstanding by biologists and biochemists, a new term "protion" has been introduced to denote such abstract objects in M systems in (Sosik et al, 2018). Third, the primary goal in studying M systems, as given by sets of elementary objects with their rules of interaction in a host geometric space (e.g., ordinary 2D or 3D space), is to examine and characterize the behavior of larger and more complex objects and systems emerging as a result of the interaction of component objects according to a given set of reaction/production rules and environmental conditions they are placed in, including nutrients.…”

“…A typical reaction rule has the form u → v , where u (reactants) and v (products) are multisets which may contain floating objects, protions, and/or tiles. A more detailed, but also more technical, description of M systems can be found in [ 17 , 18 ].…”

“…Motivated by these considerations, [ 17 , 18 ] recently proposed a dynamic computational model, M systems, based in part on the techniques of membrane computing [ 19 ]. M systems arose as an evolution of so-called membrane systems (or P systems, [ 19 ]), which generally consist of a structure of (possibly nested) delimiting regions in 2D or 3D space enclosed by membranes, as illustrated below, and as a mathematical abstraction of common biological structures.…”