The evolution of future wealth.
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Journal Article↗
Biomedical subjects
Stuart A Kauffman
Publications and source records attributed to Stuart A Kauffman.
A general modeling strategy for gene regulatory networks with stochastic dynamics.
A stochastic genetic toggle switch model that consists of two identical, mutually repressive genes is built using the Gillespie algorithm with time delays as an example of a simple stochastic gene regulatory network. The stochastic kinetics of this model is investigated, and it is found that the delays for the protein productions can highly weaken the global fluctuations for the expressions of the two genes, making the two mutually repressive genes coexist for a long time. Starting from this model, we propose a practical modeling strategy for more complex gene regulatory networks. Unlike previous applications of the Gillespie algorithm to simulate specific genetic networks dynamics, this modeling strategy is proposed for an ensemble approach to study the dynamical properties of these networks. The model allows any combination of gene expression products, forming complex multimers, and each one of the multimers is assigned to a randomly chosen gene promoter site as an activator or inhibitor. In addition, each gene, although it has only one promoter site, can have multiple regulatory sites and distinct rates of translation and transcription. Also, different genes have different time delays for transcription and translation and all reaction constant rates are initially randomly chosen from a range of values. Therefore, the general strategy here proposed may be used to simulate real genetic networks.
Algorithms↗
Phase transition in random catalytic networks.
The notion of (auto)catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this long-standing problem is possible by mapping the problem onto a set of nonlinear recurrence equations. The solution of these equations shows a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to fully understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other. We observe a remarkable similarity of the solution of the system and the PVT diagrams in standard thermodynamics.
Algorithms↗
Eukaryotic cells are dynamically ordered or critical but not chaotic.
Two important theoretical approaches have been developed to generically characterize the relationship between the structure and function of large genetic networks: the continuous approach, based on reaction-kinetics differential equations, and the Boolean approach, based on difference equations and discrete logical rules. These two approaches do not always coincide in their predictions for the same system. Nonetheless, both of them predict that the highly nonlinear dynamics exhibited by genetic regulatory systems can be characterized into two broad regimes, to wit, an ordered regime where the system is robust against perturbations, and a chaotic regime where the system is extremely sensitive to perturbations. It has been a plausible and long-standing hypothesis that genomic regulatory networks of real cells operate in the ordered regime or at the border between order and chaos. This hypothesis is indirectly supported by the robustness and stability observed in the phenotypic traits of living organisms under genetic perturbations. However, there has been no systematic study to determine whether the gene-expression patterns of real cells are compatible with the dynamically ordered regimes predicted by theoretical models. Using the Boolean approach, here we show what we believe to be the first direct evidence that the underlying genetic network of HeLa cells appears to operate either in the ordered regime or at the border between order and chaos but does not appear to be chaotic.
Gene Expression Regulation↗
Activities and sensitivities in boolean network models.
We study how the notions of importance of variables in Boolean functions as well as the sensitivities of the functions to changes in these variables impact the dynamical behavior of Boolean networks. The activity of a variable captures its influence on the output of the function and is a measure of that variable's importance. The average sensitivity of a Boolean function captures the smoothness of the function and is related to its internal homogeneity. In a random Boolean network, we show that the expected average sensitivity determines the well-known critical transition curve. We also discuss canalizing functions and the fact that the canalizing variables enjoy higher importance, as measured by their activities, than the noncanalizing variables. Finally, we demonstrate the important role of the average sensitivity in determining the dynamical behavior of a Boolean network.
Logic↗
Adaptive walks in a gene network model of morphogenesis: insights into the Cambrian explosion.
The emergence of complex patterns of organization close to the Cambrian boundary is known to have happened over a (geologically) short period of time. It involved the rapid diversification of body plans and stands as one of the major transitions in evolution. How it took place is a controversial issue. Here we explore this problem by considering a simple model of pattern formation in multicellular organisms. By modeling gene network-based morphogenesis and its evolution through adaptive walks, we explore the question of how combinatorial explosions might have been actually involved in the Cambrian event. Here we show that a small amount of genetic complexity including both gene regulation and cell-cell signaling allows one to generate an extraordinary repertoire of stable spatial patterns of gene expression compatible with observed anteroposterior patterns in early development of metazoans. The consequences for the understanding of the tempo and mode of the Cambrian event are outlined.
Adaptation, Physiological↗