Improving Universality Results on Parallel Enzymatic Numerical P Systems

We improve previously known universality results on enzymatic numerical P systems (EN P systems, for short) working in all-parallel and one-parallel modes. By using a attening technique, we rst show that any EN P system working in one of these modes can be simulated by an equivalent one-membrane EN P system working in the same mode. Then we show that linear production functions, each depending upon at most one variable, su ce to reach universality for both computing modes. As a byproduct, we propose some small deterministic universal enzymatic numerical P systems

Improving the Universality Results of Enzymatic Numerical P Systems

This paper provides the proof that Enzymatic Numerical P Sytems with deterministic, but parallel, execution model are universal, even when the production functions used are polynomials of degree 1. This extends previous known results and provides the optimal case in terms of polynomial degree

Geometric Universality of Currents

We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that under the assumption of constancy of the relative rates, the system demonstrates a profound statistical symmetry, resulting in geometric universality of the statistics of the particle currents. This phenomenon applies broadly to many man-made and natural open stochastic systems, such as queuing of packages over the internet, transport of electrons and quasi-particles in mesoscopic systems, and chains of reactions in bio-chemical networks. We illustrate the utility of our general approach using two enabling examples from the two latter disciplines.Comment: 15 pages, 5 figure

Open Problems, Research Topics, Recent Results on Numerical and Spiking Neural P Systems (The "Curtea de Arge s 2015 Series")

A series of open problems and research topics are formulated, about numer- ical and spiking neural P systems, initially prepared as a working material for a three months research stage of the second and the third co-author in Curtea de Arge s, Roma- nia, in the fall of 2015. Further problems were added during this period, while certain problems were addressed in this time; some details and references are provided for such cases

Error thresholds for self- and cross-specific enzymatic replication

The information content of a non-enzymatic self-replicator is limited by Eigen's error threshold. Presumably, enzymatic replication can maintain higher complexity, but in a competitive environment such a replicator is faced with two problems related to its twofold role as enzyme and substrate: as enzyme, it should replicate itself rather than wastefully copy non-functional substrates, and as substrate it should preferably be replicated by superior enzymes instead of less-efficient mutants. Because specific recognition can enforce these propensities, we thoroughly analyze an idealized quasispecies model for enzymatic replication, with replication rates that are either a decreasing (self-specific) or increasing (cross-specific) function of the Hamming distance between the recognition or "tag" sequences of enzyme and substrate. We find that very weak self-specificity suffices to localize a population about a master sequence and thus to preserve its information, while simultaneous localization about complementary sequences in the cross-specific case is more challenging. A surprising result is that stronger specificity constraints allow longer recognition sequences, because the populations are better localized. Extrapolating from experimental data, we obtain rough quantitative estimates for the maximal length of the recognition or tag sequence that can be used to reliably discriminate appropriate and infeasible enzymes and substrates, respectively.Comment: 23 pages, 7 figures; final version as publishe

Universal features of cell polarization processes

Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions. An example which has been thoroughly studied is the formation of signaling domains during eukaryotic chemotaxis. In this case, the process of domain growth may be described by the use of a constrained time-dependent Landau-Ginzburg equation, admitting scale-invariant solutions {\textit{\`a la}} Lifshitz and Slyozov. The constraint results here from a mechanism of fast cycling of molecules between a cytosolic, inactive state and a membrane-bound, active state, which dynamically tunes the chemical potential for membrane binding to a value corresponding to the coexistence of different phases on the cell membrane. We provide here a universal description of this process both in the presence and absence of a gradient in the external activation field. Universal power laws are derived for the time needed for the cell to polarize in a chemotactic gradient, and for the value of the smallest detectable gradient. We also describe a concrete realization of our scheme based on the analysis of available biochemical and biophysical data.Comment: Submitted to Journal of Statistical Mechanics -Theory and Experiment

Unzipping DNA - towards the first step of replication

The opening of the Y-fork - the first step of DNA replication - is shown to be a critical phenomenon under an external force at one of its ends. From the results of an equivalent delocalization in a non-hermitian quantum-mechanics problem we show the different scaling behavior of unzipping and melting. The resultant long-range critical features within the unzipped part of Y might play a role in the highly correlated biochemical functions during replication.Comment: 4 pages, revtex, 2 eps figure