A mathematical model was developed to relate the degradation trend of bioresorbable polymers to different underlying hydrolysis mechanisms, including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. The effect of each mechanism on molecular weight degradation and potential mass loss was analysed. A simple scheme was developed ...

The emergence of autocatalytic structures in model chemistries has been a prominent subject throughout the history of artificial life research (Rasmussen (1985); Farmer et al. (1986); Kauffman (1986); Rasmussen (1989); Hordijk et al. (2011) and others). Most of these works have been concerned with the likelihood of finding autocatalytic sets in a population of random cross-catalytic molecules. ...

The regulation of the cell cycle clock is examined using a theoretical model for the embryonic cell cycle, where the clock is described as a single-limit cycle [1]. By taking the coefficient of the autocatalytic reaction as proportional to the deviation of the system from its equilibrium state, we show how such clocks can be adjusted to function on several time scales. This feedback control, ca...

Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autoc...

The ability of systems of molecular reactions to be simultaneously autocatalylic and sustained by some ambient 'food source' of simple molecules may have been an essential step in the origin of life. In this paper we first describe a polynomial-time algorithm that determines whether any given set of molecules, reactions and catalysations contains a subsystem that is both autocatalytic and able ...

A problem of self-referential paradox and self-reproduction is discussed in a network model of machines and tapes. A tape consists of a bit string, encoding function of a machine. Tapes are replicated when it is attached by an adequate machine. Generally, a tape is replicated but it may be di erent from the original one. In this paper, external noise evolves diversity in a system. New reaction ...

Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of cooperative molecular species arises and evolves to become more complex and structured. The network is modeled by a directed weighted graph whose positive and ...

A new type of out-of-phase oscillatory Turing pattern is found in simulations of a simple two-variable model of a bistable reaction-diffusion system consisting of an autocatalytic activator reacting with a substrate that is replenished by a flow. This class of models can describe pH oscillators or enzymatic reactions. No Hopf instability is necessary for this type of oscillatory Turing pattern.