Membrane systems with limited parallelism

Membrane computing is an emerging research field that belongs to the more general area of molecular computing, which deals with computational models inspired from bio-molecular processes. Membrane computing aims at defining models, called membrane systems or P systems, which abstract the functioning and structure of the cell. A membrane system consists of a hierarchical arrangement of membranes delimiting regions, which represent various compartments of a cell, and with each region containing bio-chemical elements of various types and having associated evolution rules, which represent bio-chemical processes taking place inside the cell. This work is a continuation of the investigations aiming to bridge membrane computing (where in a compartmental cell-like structure the chemicals to evolve are placed in compartments defined by membranes) and brane calculi (where one considers again a compartmental cell-like structure with the chemicals/proteins placed on the membranes themselves). We use objects both in compartments and on membranes (the latter are called proteins), with the objects from membranes evolving under the control of the proteins. Several possibilities are considered (objects only moved across membranes or also changed during this operation, with the proteins only assisting the move/change or also changing themselves). Somewhat expected, computational universality is obtained for several combinations of such possibilities. We also present a method for solving the NP-complete SAT problem using P systems with proteins on membranes. The SAT problem is solved in O(nm) time, where n is the number of boolean variables and m is the number of clauses for an instance written in conjunctive normal form. Thus, we can say that the solution for each given instance is obtained in linear time. We succeeded in solving SAT by a uniform construction of a deterministic P system which uses rules involving objects in regions, proteins on membranes, and membrane division. Then, we investigate the computational power of P systems with proteins on membranes in some particular cases: when only one protein is placed on a membrane, when the systems have a minimal number of rules, when the computation evolves in accepting or computing mode, etc. This dissertation introduces also another new variant of membrane systems that uses context-free rewriting rules for the evolution of objects placed inside compartments of a cell, and symport rules for communication between membranes. The strings circulate across membranes depending on their membership to regular languages given by means of regular expressions. We prove that these rewriting-symport P systems generate all recursively enumerable languages. We investigate the computational power of these newly introduced P systems for three particular forms of the regular expressions that are used by the symport rules. A characterization of ET0L languages is obtained in this context

Minimal cooperation in polarizationless P systems with active membranes

P systems with active membranes is a well developed framework in the eld of Membrane Computing. Using evolution, communication, dissolution and division rules, we know that some kinds of problems can be solved by those systems, but taking into account which ingredients are used. All these rules are inspired by the behavior of living cells, who \compute" with their proteins in order to obtain energy, create components, send information to other cells, kill themselves (in a process called apoptosis), and so on. But there are other behaviors not captured in this framework. As mitosis is simulated by division rules (for elementary and non-elementary membranes), meiosis, that is, membrane ssion inspiration is captured in separation rules. It di ers from the rst in the sense of duplication of the objects (that is, in division rules, we duplicate the objects not involved in the rule, meanwhile in separation rules we divide the content of the original membrane into the new membranes created). Evolution rules simulate the transformation of components in membranes, but it is well known that elements interact with another ones in order to obtain new components. Cooperation in evolution rules is considered. More speci cally, minimal cooperation (in the sense that only two objects can interact in order to create one or two objects

De novo vesicle formation and growth: an integrative approach to artificial cells.

The assembly of artificial cells provides a novel strategy to reconstruct life's functions and shed light on how life emerged on Earth and possibly elsewhere. A major challenge to the development of artificial cells is the establishment of simple methodologies to mimic native membrane generation. An ambitious strategy is the bottom-up approach, which aims to systematically control the assembly of highly ordered membrane architectures with defined functionality. This perspective will cover recent advances and the current state-of-the-art of minimal lipid architectures that can faithfully reconstruct the structure and function of living cells. Specifically, we will overview work related to the de novo formation and growth of biomimetic membranes. These studies give us a deeper understanding of the nature of living systems and bring new insights into the origin of cellular life

Limits on P Systems with Proteins and Without Division

In the field of Membrane Computing, computational complexity theory has been widely studied trying to nd frontiers of efficiency by means of syntactic or semantical ingredients. The objective of this is to nd two kinds of systems, one non-efficient and another one, at least, presumably efficient, that is, that can solve NP-complete prob- lems in polynomial time, and adapt a solution of such a problem in the former. If it is possible, then P = NP. Several borderlines have been defi ned, and new characterizations of different types of membrane systems have been published. In this work, a certain type of P system, where proteins act as a supporting element for a rule to be red, is studied. In particular, while division rules, the abstraction of cellular mitosis is forbidden, only problems from class P can be solved, in contrast to the result obtained allowing them.Ministerio de Economía y Competitividad TIN2017-89842-PNational Natural Science Foundation of China No 6132010600

Synthetic Biology: A Bridge between Artificial and Natural Cells.

Artificial cells are simple cell-like entities that possess certain properties of natural cells. In general, artificial cells are constructed using three parts: (1) biological membranes that serve as protective barriers, while allowing communication between the cells and the environment; (2) transcription and translation machinery that synthesize proteins based on genetic sequences; and (3) genetic modules that control the dynamics of the whole cell. Artificial cells are minimal and well-defined systems that can be more easily engineered and controlled when compared to natural cells. Artificial cells can be used as biomimetic systems to study and understand natural dynamics of cells with minimal interference from cellular complexity. However, there remain significant gaps between artificial and natural cells. How much information can we encode into artificial cells? What is the minimal number of factors that are necessary to achieve robust functioning of artificial cells? Can artificial cells communicate with their environments efficiently? Can artificial cells replicate, divide or even evolve? Here, we review synthetic biological methods that could shrink the gaps between artificial and natural cells. The closure of these gaps will lead to advancement in synthetic biology, cellular biology and biomedical applications

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism

A Process Algebraical Approach to Modelling Compartmentalized Biological Systems

This paper introduces Protein Calculus, a special modeling language designed for encoding and calculating the behaviors of compartmentilized biological systems. The formalism combines, in a unified framework, two successful computational paradigms - process algebras and membrane systems. The goal of Protein Calculus is to provide a formal tool for transforming collected information from in vivo experiments into coded definition of the different types of proteins, complexes of proteins, and membrane-organized systems of such entities. Using this encoded information as input, our calculus computes, in silico, the possible behaviors of a living system. This is the preliminary version of a paper that was published in Proceedings of International Conference of Computational Methods in Sciences and Engineering (ICCMSE), American Institute of Physics, AIP Proceedings, N 2: 642-646, 2007 (http://scitation.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=963&Issue=2)

ESCRT-III mediated cell division in Sulfolobus acidocaldarius - a reconstitution perspective

In the framework of synthetic biology, it has become an intriguing question what would be the minimal representation of cell division machinery. Thus, it seems appropriate to compare how cell division is realized in different microorganisms. Inparticular, the cell division system of Crenarchaeota lacks certain proteins found in most bacteria and Euryarchaeota, such as FtsZ, MreB or the Min system. The Sulfolobaceae family encodes functional homologs of the eukaryotic proteins vacuolar protein sorting 4(Vps4) and endosomal sorting complex required for transport-III (ESCRT-III). ESCRT-III is essential for several eukaryotic pathways, e.g., budding of intraluminal vesicles, or cytokinesis, whereas Vps4 dissociates the ESCRT-III complex from the membrane. Cell Division A(CdvA) is required for the recruitment of crenarchaeal ESCRT-III proteins to the membrane at mid-cell. The proteins polymerize and form a smaller structure during constriction. Thus, ESCRT-III mediated cell division in Sulfolobus acidocaldarius shows functional analogies to the Z ring observed in prokaryotes like Escherichia coli, which has recently begun to be reconstituted in vitro. In this short perspective, we discuss the possibility of building such an in vitro cell division system on basis of archaeal ESCRT-III

Open and cut: allosteric motion and membrane fission by dynamin superfamily proteins.

Cells have evolved diverse protein-based machinery to reshape, cut, or fuse their membrane-delimited compartments. Dynamin superfamily proteins are principal components of this machinery and use their ability to hydrolyze GTP and to polymerize into helices and rings to achieve these goals. Nucleotide-binding, hydrolysis, and exchange reactions drive significant conformational changes across the dynamin family, and these changes alter the shape and stability of supramolecular dynamin oligomers, as well as the ability of dynamins to bind receptors and membranes. Mutations that interfere with the conformational repertoire of these enzymes, and hence with membrane fission, exist in several inherited human diseases. Here, we discuss insights from new x-ray crystal structures and cryo-EM reconstructions that have enabled us to infer some of the allosteric dynamics for these proteins. Together, these studies help us to understand how dynamins perform mechanical work, as well as how specific mutants of dynamin family proteins exhibit pathogenic properties