Bistability, and more generally multistability, is a key system dynamics feature enabling decision-making and memory in cells. Deciphering the molecular determinants of multistability is thus crucial for a better understanding of cellular pathways and their (re)engineering in synthetic biology. Here, we show that a key motif found predominantly in eukaryotic signalling systems, namely a futile ...

We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.

In the August issue of TiPS, Epand and Lester analysed the effect of the physicochemical properties of the membrane on protein kinase C activity. In addition to those substrates discussed that require the presence of Ca2+ and phospholipids, other substrates can be phosphorylated in the absence of these activators. It is possible that this differential substrate requirement could be exploited ph...

The binary hypercube Qn has small diameter, but a relatively large number of links. Because of this, efforts have been made to determine the maximum number of links that can be deleted without increasing the diameter. However, the resulting networks are not vertex-symmetric. We propose a family of vertex-symmetric spanning subnetworks of Qn, whose diameter differs from that of Qn by only a smal...

(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...

We consider simple cube-curves in the orthogonal 3D grid of cells. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve’s length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far only one general algorithm called rubber-band algorithm was known ...

In this paper, we investigate sufficient conditions on the neighborhood of independent vertices which imply that a graph contains k independent cycles or chorded cycles. This is related to several results of Corrádi and Hajnal, Justesen, Wang, and Faudree and Gould on graphs containing k independent cycles, and Finkel on graphs containing k chorded cycles. In particular, we establish that if in...

Let N = {1, 2, 3, · · · } denote the natural numbers. Given integers e ≥ 1 and b ≥ 2, let x = ∑n i=0 aib i with 0 ≤ ai ≤ b − 1 (thus ai are the digits of x in base b). We define the happy function Se,b : N −→ N by