Genetic networks with canalyzing Boolean rules are always stable

Abstract

We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are dynamically stable. Furthermore, for architectures with few inputs per node, the dynamics of the networks is close to critical. In addition, the fraction of genes that are active decreases with the number of inputs per node. These results are based upon investigating ensembles of networks using analytical methods. Also, for different in-degree distributions, the numbers of fixed points and cycles are calculated, with results intuitively consistent with stability analysis; fewer inputs per node implies more cycles, and vice versa. There are hints that genetic networks acquire broader degree distributions with evolution, and hence our results indicate that for single cells, the dynamics should become more stable with evolution. However, such an effect is very likely compensated for by multicellular dynamics, because one expects less stability when interactions among cells are included. We verify this by simulations of a simple model for interactions among cells.

Canalization and symmetry in Boolean models for genetic regulatory networks

“…Here, the effective connectivity of the gene depends on the current state of the network. More complex categories are also possible, such as the nested canalizing functions proposed by Kauffman [19,26]. Since the fraction of canalizing functions drops rapidly with k, as shown in Ref.…”

Superstability of the yeast cell-cycle dynamics: Ensuring causality in the presence of biochemical stochasticity

“…The yeast cell-cycle is remarkably robust in this sense [17]. Other approaches to assessing robustness in biological networks include local stability and bifurcation analyses [8], stability under node state perturbation [3,11] and probabilistic Boolean networks [20]. In this work we will concentrate on the robustness under stochastically varying processing times (for protein concentration buildup and decay) as was considered in [15].…”

Biologie des systèmes et applications médicales

“…Soit C le nombre de ses composantes fortement connexes comportant un circuit positif, A le nombre de ses attracteurs, K = I/n sa connectivité, c'est-à-dire le rapport entre les nombres I d'interactions et n de gènes, et P le nombre de ses circuits positifs, en ne comptant qu'une fois ceux qui partagent un gène. Nous avons alors les conjectures : 2 P ≥ A ≥ 2 C et A ≥ O(n 1/2 ), valables dans les graphes de type Hopfield, dont les fonctions de transition sont du type majorité pondérée [15][16][17][18][19][20][21][22] et dans les graphes de type Kauffman, dont les fonctions de transition sont toutes les fonctions booléennes possibles [6,[23][24][25]. Dans les réseaux constitués de couches successives de gènes se co-exprimant, on peut montrer que la borne supérieure peut être remplacée par 2 V , où V est le nombre de gènes de la première couche [22].…”