On the power of P systems with active membranes using weak non-elementary membrane division

It is known that polarizationless P systems with active membranes can solve $$\mathrm {PSPACE}$$ PSPACE -complete problems in polynomial time without using in-communication rules but using the classical (also called strong) non-elementary membrane division rules. In this paper, we show that this holds also when in-communication rules are allowed but strong non-elementary division rules are replaced with weak non-elementary division rules, a type of rule which is an extension of elementary membrane divisions to non-elementary membranes. Since it is known that without in-communication rules, these P systems can solve in polynomial time only problems in $$\mathrm {P}^{\text {NP}}$$ P NP , our result proves that these rules serve as a borderline between $$\mathrm {P}^{\text {NP}}$$ P NP and $$\mathrm {PSPACE}$$ PSPACE concerning the computational power of these P systems.

A new method to simulate restricted variants of polarizationless P systems with active membranes

According to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve $${\mathbf {NP}}$$NP-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

Minimal Parallelism and Number of Membrane Polarizations

It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal.

Dynamin-related Protein 1 (Drp1) Promotes Structural Intermediates of Membrane Division

Drp1 is a dynamin-like GTPase that mediates mitochondrial and peroxisomal division in a process dependent on self-assembly and coupled to GTP hydrolysis. Despite the link between Drp1 malfunction and human disease, the molecular details of its membrane activity remain poorly understood. Here we reconstituted and directly visualized Drp1 activity in giant unilamellar vesicles. We quantified the effect of lipid composition and GTP on membrane binding and remodeling activity by fluorescence confocal microscopy and flow cytometry. In contrast to other dynamin relatives, Drp1 bound to both curved and flat membranes even in the absence of nucleotides. We also found that Drp1 induced membrane tubulation that was stimulated by cardiolipin. Moreover, Drp1 promoted membrane tethering dependent on the intrinsic curvature of the membrane lipids and on GTP. Interestingly, Drp1 concentrated at membrane contact surfaces and, in the presence of GTP, formed discrete clusters on the vesicles. Our findings support a role of Drp1 not only in the formation of lipid tubes but also on the stabilization of tightly apposed membranes, which are intermediate states in the process of mitochondrial fission.