Evolution of Developmental Canalization in Networks of Competing Boolean Nodes

Bassler, Kevin E.; Lee, Choongseop; Lee, I. Yong

doi:10.1103/physrevlett.93.038101

Cited by 22 publications

(41 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a simulation study of the evolution properties of the different Boolean functions, Bassler et al [29] observed that functions with k = 3 inputs fell into 14 distinct classes. In their study all of the functions that were members of the same class evolved, on average, with equal probability.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Canalization and symmetry in Boolean models for genetic regulatory networks

Reichhardt

Bassler

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Abstract. Canalization of genetic regulatory networks has been argued to be favored by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial canalization can arise in purely random networks in the absence of evolutionary pressures. We use a mapping of the Boolean functions in the Kauffman N-K model for genetic regulatory networks onto a k−dimensional Ising hypercube (where k = K) to show that the functions can be divided into different classes strictly due to geometrical constraints. The classes can be counted and their properties determined using results from group theory and isomer chemistry. We demonstrate that partially canalizing functions completely dominate all possible Boolean functions, particularly for higher k. This indicates that partial canalization is extremely common, even in randomly chosen networks, and has implications for how much information can be obtained in experiments on native state genetic regulatory networks.

show abstract

Section: Resultsmentioning

confidence: 99%

“…In mathematical terms, the classes that were identified empirically in Ref. [29] are group orbits. We illustrate the mapping for the sixteen k = 2 functions in figure 2, where the rotational plus parity symmetries of the functions belonging to each of the four classes are obvious.…”

Section: Resultsmentioning

confidence: 99%

Canalization and symmetry in Boolean models for genetic regulatory networks

Reichhardt

Bassler

2007

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…These 14 Zyklenzeiger classes are labeled from A to J, according to the canalization properties of the functions in the class. Additionally, those functions labeled C, F , and H, form multiple classes, designated with subscripts, to distinguish those with the same canalization properties but different internal homogeneity and parity symmetry [51]. The 10 function classes of critical network dynamics result from combining the Zyklenzeiger classes designated with subscripts.…”

Section: Symmetry In Other Dynamicsmentioning

confidence: 99%

Symmetry in critical random Boolean network dynamics

2014

View full text Add to dashboard Cite

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems.

show abstract

“…The mutations affect the connections and the update functions of the nodes. Compared to the simulations in [8,9,10,11,12,13,14,15,16], fitness can be changed by more types of mutations in our model. We let the networks evolve freely under a biologically motivated fitness criterion without imposing any "target properties" to find network topologies that are evolutionary robust.…”

Section: Introductionmentioning

confidence: 99%

“…The network evolves to a stationary state "at the edge of chaos". Further studies of the model [13] showed that the evolved networks are highly canalized. Other models that evolve to a critical state are studied in [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Evolution of canalizing Boolean networks

Szejka¹,

Drossel²

2007

Eur. Phys. J. B

View full text Add to dashboard Cite

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk, which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having such a high degree of robustness, the evolved networks still share many features with "chaotic" networks.

show abstract

Evolution of Developmental Canalization in Networks of Competing Boolean Nodes

Cited by 22 publications

References 28 publications

Canalization and symmetry in Boolean models for genetic regulatory networks

Canalization and symmetry in Boolean models for genetic regulatory networks

Symmetry in critical random Boolean network dynamics

Evolution of canalizing Boolean networks

Contact Info

Product

Resources

About