Membrane fission versus cell division: When membrane proliferation is not enough

Cell division is a process that produces two or more cells from one cell by replicating the original chromosomes so that each daughter cell gets a copy of them. Membrane fission is a process by which a biological membrane is split into two new ones in suchamanner that the contents of the initial membrane get distributedor separated among the new membranes. Inspired by these biological phenomena, new kinds of models we reconsidered in the discipline of Membrane Computing, in the context of P systems with active membranes, and tissue P systems that use symport/antiport rules, respectively. This paper combines the two approaches: cell-like P systems with symport/antiport rules and membrane separation are studied, from a computational complexity perspective.Specifically, the role of the environment in the context of cell-like P systems withmembrane separation is established, and additional borderlines between tractability and NP-hardness are summarized.Ministerio de Economía y Competitividad TIN2012- 3743

Computational Complexity Theory in Membrane Computing: Seventeen Years After

In this work we revisit the basic concepts, definitions of computational complexity theory in membrane computing. The paper also discusses a novel methodology to tackle the P versus NP problem in the context of the aforementioned theory. The methodology is illustrated with a collection of frontiers of tractability for several classes of P systems.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Tissue-like P Systems Without Environment

In this paper we present a tissue-like P systems model with cell division the environment has been replaced by an extra cell. In such model, we present a uniform family of recognizer P systems which solves the Subset Sum problem. This solution establishes a new frontier for the tractability of computationally hard problems in Membrane Computing, since it proves that NP-complete problems can be solved without an arbitrarily large amount of objects in the environment.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-0420

The role of topology and mechanics in uniaxially growing cell networks

In biological systems, the growth of cells, tissues, and organs is influenced by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous environment as cells pull and push their neighbors in a cell network. Despite this local heterogeneity, at the tissue level, the cell network is remarkably robust, as it is not easily perturbed by changes in the mechanical environment or the network connectivity. Through a network model, we relate global tissue structure (i.e. the cell network topology) and local growth mechanisms (growth laws) to the overall tissue response. Within this framework, we investigate the two main mechanical growth laws that have been proposed: stress-driven or strain-driven growth. We show that in order to create a robust and stable tissue environment, networks with predominantly series connections are naturally driven by stress-driven growth, whereas networks with predominantly parallel connections are associated with strain-driven growth

The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in the framework of tissue P systems with evolutional communication rules.The computational complexity of this kind of P systems is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with evolutional communication rules of length at most (��, 1), for each natural number �� ≥ 1. In the case where that length is upper bounded by (3, 2), a polynomial time solution to the SAT problem is provided, hence, assuming that P ̸= NP a new boundary between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution to the SAT problem

Limits of the power of Tissue P systems with cell division

Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph. Basic opera- tions in these systems are communication rules, enriched in some variants with cell division or cell separation. Several variants of tissue P systems were recently studied, together with the concept of uniform families of these systems. Their computational power was shown to range between P and NP ? co-NP , thus characterizing some interesting borderlines between tractability and intractability. In this paper we show that com- putational power of these uniform families in polynomial time is limited by the class PSPACE . This class characterizes the power of many clas- sical parallel computing model

The role of integral membrane proteins in computational complexity theory

In the framework of Membrane Computing, several tools to tackle the P versus NP problems by means of frontiers of the efficiency expressed in terms of syntactic or semantic ingredients, have been developed. In this paper, an overview of the results in computational complexity theory concerning to membrane systems (tissuelike and cell-like approach) with symport/antiport rules (where objects are transported without evolving), is given. The frontiers are formulated regarding the length of communication rules, the kind of rules implementing the production of an exponential number of cells/membranes in polynomial time, and the role of the environment. An interesting remark of the obtained results refers that the underlying structure to membrane systems (directed graph versus rooted tree) does not matter in this context.Ministerio de Economía, Industria y Competitividad TIN2017-89842-P (MABICAP)National Natural Science Foundation of China No. 6132010600

A new perspective on computational complexity theory in Membrane Computing

A single Turing machine can solve decision problems with an in nite number of instances. On the other hand, in the framework of membrane computing, a \solution" to an abstract decision problem consists of a family of membrane systems (where each system of the family is associated with a nite set of instances of the problem to be solved). An interesting question is to analyze the possibility to nd a single membrane system able to deal with the in nitely many instances of a decision problem. In this context, it is fundamental to de ne precisely how the instances of the problem are introduced into the system. In this paper, two different methods are considered: pre-computed (in polynomial time) resources and non-treated resources. An extended version of this work will be presented in the 20th International Conference on Membrane Computing.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Efficient simulation of tissue-like P systems by transition cell-like P systems

In the framework of P systems, it is known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP-complete problems. Nonetheless, it could be sufficient to create an exponential number of membranes in polynomial time. Working with P systems whose membrane structure does not increase in size, it is known that it is not possible to solve computationally hard problems (unless P = NP), basically due to the impossibility of constructing exponential number of membranes, in polynomial time, using only evolution, communication and dissolution rules. In this paper we show how a family of recognizer tissue P systems with symport/ antiport rules which solves a decision problem can be efficiently simulated by a family of basic recognizer P systems solving the same problem. This simulation allows us to transfer the result about the limitations in computational power, from the model of basic cell-like P systems to this kind of tissue-like P systems.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58