We consider the problem of estimating Boolean models of gene regulation networks from few and noisy mea surements. To this end, we use a representation of Boolean functions as multi-af fi ne polynomials, leading to a reformulation of the estimation problem as mixed integer linear program. We then show that the integer constraints can be omitted which improves existing results and reduces the required computing time drastically. Also certain properties of Boolean functions such as unateness or the canalizing property can be included in the linear formulation. The benefits of this reformulation are demonstrated with the help of a large Boolean model of the network of the segment polarity genes in Drosophila melanogaster.
Bi-or even multistable behavior is a recurrent phenomenon in gene regulation networks. These networks have the capacity to operate in two or more distinct modes in a stable manner. In this work, we consider gene regulation networks with known interaction structure but unknown reaction kinetics. Additionally, it is assumed that several distinct operation modes were observed experimentally whereby also the measurements of the individual protein concentrations are uncertain. For this setup, the important question of model validation is addressed: Can the given network structure in principle reproduce the observed operation modes? To approach this problem, the work builds on an existing modeling framework [4] which is appropriate to deal with uncertain gene regulation networks. By regarding each operation mode as a forward-invariant set in the state space and with the notion of compatible intervals, it is shown how the validation problem can be translated into a combinatorial one. An algorithm is developed which can efficiently solve the new problem. Finally, the well-known bistable lactose utilization network is analyzed with this new method.
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