Neutral space analysis for a Boolean network model of the fission yeast cell cycle network

Background

Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle.

Results

Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G₁ fixed point was found for deterministic updating schemes.

Conclusions

In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.     

An in silico target identification using Boolean network attractors: Avoiding pathological phenotypes

Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.     

Persistence despite perturbations for interacting populations

Two definitions of persistence despite perturbations in deterministic models are presented. The first definition, persistence despite frequent small perturbations, is shown to be equivalent to the existence of a positive attractor i.e. an attractor bounded away from extinction. The second definition, persistence despite rare large perturbations, is shown to be equivalent to permanence i.e. a positive attractor whose basin of attraction includes all positive states. Both definitions set up a natural dichotomy for classifying models of interacting populations. Namely, a model is either persistent despite perturbations or not. When it is not persistent, it follows that all initial conditions are prone to extinction due to perturbations of the appropriate type. For frequent small perturbations, this method of classification is shown to be generically robust: there is a dense set of models for which persistent (respectively, extinction prone) models lies within an open set of persistent (resp. extinction prone) models. For rare large perturbations, this method of classification is shown not to be generically robust. Namely, work of Josef Hofbauer and the author have shown there are open sets of ecological models containing a dense sets of permanent models and a dense set of extinction prone models. The merits and drawbacks of these different definitions are discussed.     

On the concept of attractor for community-dynamical processes I: the case of unstructured populations

We introduce a notion of attractor adapted to dynamical processes as they are studied in community-ecological models and their computer simulations. This attractor concept is modeled after that of Ruelle as presented in [11] and [12]. It incorporates the fact that in an immigration-free community populations can go extinct at low values of their densities.Mathematics Subject Classification (2000):37b20, 37c50, 37c70     

In search of sports biomechanics’ holy grail: Can athlete-specific optimum sports techniques be identified?

The development of methods that can identify athlete-specific optimum sports techniques—arguably the holy grail of sports biomechanics—is one of the greatest challenges for researchers in the field. This ‘perspectives article’ critically examines, from a dynamical systems theoretical standpoint, the claim that athlete-specific optimum sports techniques can be identified through biomechanical optimisation modelling. To identify athlete-specific optimum sports techniques, dynamical systems theory suggests that a representative set of organismic constraints, along with their non-linear characteristics, needs to be identified and incorporated into the mathematical model of the athlete. However, whether the athlete will be able to adopt, and reliably reproduce, his/her predicted optimum technique will largely be dependent on his/her intrinsic dynamics. If the attractor valley corresponding to the existing technique is deep, or if the attractor valleys corresponding to the existing technique and the predicted optimum technique are in different topographical regions of the dynamic landscape, technical modifications may be challenging or impossible to reliably implement even after extended practice. The attractor layout defining the intrinsic dynamics of the athlete, therefore, needs to be determined to establish the likelihood of the predicted optimum technique being reliably attainable by the athlete. Given the limited set of organismic constraints typically used in mathematical models of athletes, combined with the methodological challenges associated with mapping the attractor layout of an athlete, it seems unlikely that athlete-specific optimum sports techniques will be identifiable through biomechanical optimisation modelling for the majority of sports skills in the near future.